Información del autor
Autor Montesinos Amilibia, José María |
Documentos disponibles escritos por este autor (111)
texto impreso
Let M denote a p-fold, branched, cyclic, covering space of S3, and suppose that the three-dimensional Smith conjecture is true for p-periodic autohomeomorphisms of S3. J. S. Birman and H. M. Hilden have constructed an algorithm for deciding whet[...]texto impreso
It is shown that a PL, orientable 4-manifold with no 3- or 4-handles is a 3-fold irregular cover of the 4-ball, branched over a ribbon 2-manifold. The author also studies 2-fold branched cyclic covers and finds examples of surfaces in S4 whose 2[...]texto impreso
Montesinos Amilibia, José María ; Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa | American Mathematical Society | 1983-10This paper establishes two new ways of representing all closed orientable 3-manifolds. (1) Let F,N be a pair of disjoint bounded orientable surfaces in the 3-sphere S3. Let (Sk,Fk,Nk), k=1,2,3, be 3 copies of the triplet (S,F,N). Split S1 along [...]texto impreso
This is a survey of some consequences of the fact that the fundamental group of the orbifold with singular set the Borromean link and isotropy cyclic of order 4 is a universal Kleinian grouptexto impreso
Montesinos Amilibia, José María ; Hilden, Hugh Michael ; Tejada Jiménez, Débora María ; Toro Villegas, Margarita María | Mathematical Association of America | 2011-04It is well known that there are 17 crystallographic groups that determine the possible tessellations of the Euclidean plane. We approach them from an unusual point of view. Corresponding to each crystallographic group there is an orbifold. We sh[...]texto impreso
Motivated by applications to open manifolds and wild knots, the author in this article revisits R. H. Fox's theory [in A symposium in honor of S. Lefschetz, 243–257, Princeton Univ. Press, Princeton, N.J., 1957; MR0123298 (23 #A626)] of singular[...]texto impreso
General branched coverings, folded coverings, and branched folded coverings are all special cases of the spreads introduced by R. H. Fox in the 1950's [in A symposium in honor of S. Lefschetz, 243–257, Princeton Univ. Press, Princeton, N.J., 195[...]texto impreso
Under the framework of Fox spreads and its completions a theory thar generalizes coverings (folding covering theory) and a theroy that generalizes branched coverings (branched folding theory) is defined and some properties are proved. Two applic[...]texto impreso
Hilden, Hugh Michael ; Montesinos Amilibia, José María ; Tejada Jiménez, Débora María ; Toro Villegas, Margarita María | Academia Colombiana de Ciencias Exactas, Físicas y Naturales. | 2004A butterfly is a 3-ball B with an even number of polygonal faces, named wings, pair-wise identified. Each identification between two wings is required to be a topological reflexion whose axis is an edge shared by the wings. The set of axes of th[...]texto impreso
Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | World Scientific Publ.Co. | 2003-12The representation space or character variety of a finitely generated group is easy to define but difficult to do explicit computations with. The fundamental group of a knot can have two interesting representations into PSL2(C) coming from oppos[...]texto impreso
Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | Wiley-Blackwell | 1992A Kleinian group is a discrete subgroup of PSL(2,C). As such it acts on 3-dimensional hyperbolic space H3. A Kleinian group G is said to have finite covolume if H3/G has finite volume. An interesting subclass of Kleinian groups of finite covolum[...]texto impreso
Symmetry exists in nature and art. The rotational symmetry of a simple daisy must have at one time or another stirred geometric thoughts in the least mathematical mind. On a higher scale, the florets of Helianthus maximus naturally arrange thems[...]texto impreso
Hilden, Hugh Michael ; Montesinos Amilibia, José María ; Thickstun, Thomas L. | Pacific Journal of Mathematics | 1976The first author [Amer. J. Math. 98 (1976), no. 4, 989–992] and the second author [Quart. J. Math. Oxford Ser. (2) 27 (1976), no. 105, 85–94] have shown that any closed orientable 3-manifold M is a 3-fold cover of S3 branched over a knot. In the[...]texto impreso
Montesinos Amilibia, José María ; Whitten, Wilbur Carrington | Pacific Journal of Mathematics | 1986-12By equivariantly pasting together exteriors of links in S3 that are invariant under several different involutions of S3, we construct closed orientable 3-manifolds that are two-fold branched covering spaces of S3 in distinct ways, that is, with [...]texto impreso
Let M denote a p-fold, branched, cyclic, covering space of S3, and suppose that the three-dimensional Smith conjecture is true for p-periodic autohomeomorphisms of S3. J. S. Birman and H. M. Hilden have constructed an algorithm for deciding whet[...]texto impreso
In the late 19th century Fedorov, Schoenflies, and Barlow classified the seventeen wallpaper groups (two-dimensional crystallographic groups, five of them direct movements and twelve of them inverse movements) and the 320 three-dimensional cryst[...]texto impreso
La cristalografía es una disciplina de la geología que estudia los cristales: sus formas externas e internas; las posibilidades de estas formas, etc. Los aspectos matemáticos de la teoría son de extraordinario interés para los matemáticos porque[...]texto impreso
Let M be a closed orientable 3-manifold. The rank of M, rk(M), is the minimum number of elements that can generate ?1(M). Clearly rk(M)?Hg(M), where Hg(M) is the Heegaard genus of M. F. Waldhausen conjectured that equality holds here, but then. [...]texto impreso
Montesinos Amilibia, José María ; González Acuña, Francisco Javier | Cambridge Univ. Press | 1982-05The authors show that every knot can be embedded in codimension two in a trivial knot, and they derive corresponding theorems about embedding branched coverings in codimension two. These results (and generalizations) were obtained previously by [...]texto impreso
In this paper, the possibility of embedding a nontrivial string (R3,K) in the trivial knot (S3,U) is investigated. Uncountably many examples are given. The complementary space in S3 of the image of R3 under the embedding is a continuum. Some wel[...]texto impreso
In 1962, R. H. Fox asked [Topology of 3-manifolds and related topics (Proc. Univ. Georgia Inst., 1961), pp. 168–176, especially pp. 175–176, Prentice-Hall, Englewood Cliffs, N.J., 1962)] whether a 2-knot group could have infinitely many ends. Th[...]texto impreso
texto impreso
It is known that every closed, orientable 3-manifold contains a fi-bered knot—a simple closed curve whose complement is a surface bundle over S1. For K such a fibered knot in a rational homology 3-sphere M it is shown that for any compact subman[...]texto impreso
It is proven that every fibred link in the 3-sphere S3 with k components can be obtained as the preimage of the braid axis for a d-sheeted simple branched cover over S3, branched along a suitable closed closed braid, with d=max{k,3}. More genera[...]texto impreso
Hilden, Hugh Michael ; Montesinos Amilibia, José María ; Tejada Jiménez, Débora María ; Toro Villegas, Margarita María | Cambridge Univ Press | 2006-12-01A Fox coloured link is a pair (L,?), where L is a link in S3 and ? a simple and transitive representation of ?1(S3?L) onto the symmetric group ?3 on three elements. Here, a representation is called simple if it sends the meridians to transpositi[...]texto impreso
texto impreso
Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | Pacific Journal of Mathematics | 1997The authors discuss a class of flows on 3-manifolds closely related to Anosov flows, which they call singular Anosov flows. These are flows which are Anosov outside of a finite number of periodic "singular orbits'', such that each singular orbit[...]texto impreso
Brumfiel, G. ; Hilde, H. ; Lozano, M. T. ; Montesinos Amilibia, José María ; Ramirez, E. ; Short, H. ; Tejada Cazorla, Juan Antonio ; Toro, M. | World Scientific PublCo | 2017The main result of this paper is the construction of two Hyperbolic manifolds, M-1 and M-2, with several remarkable properties: (1) Every closed orientable 3-manifold is homeomorphic to the quotient space of the action of a group of order 16 on [...]texto impreso
Let W4=H0??H1??H2??H3?H4 be a handle decomposition of a closed, orientable PL 4-manifold. Let M4=H0??H1??H2 and let N4=N4(?)=?H3?H4=?#(S1×B3). Then W4 is M4?N4, identified along ?M4=?N4=?#(S1×S2). The first observation in this paper is that W4 d[...]texto impreso
Montesinos Amilibia, José María ; González Acuña, Francisco Javier ; Birman, Joan S. | Michigan Mathematical Journal | 1976The authors construct an infinite family of prime homology 3-spheres of Heegaard genus 2, satisfying the following two non-uniqueness properties: (1) Each of the manifolds can be structured as the 2-fold cyclic branched cover over each of two in[...]texto impreso
The author presents various ideas, proofs, constructions and tricks connected with branched coverings of 3-manifolds. After an introductory section on 2-fold branched coverings of S3 the main theme of 3-fold irregular coverings is introduced. [...]texto impreso
Long ago J. W. Alexander showed that any closed, orientable, triangulated n-manifold can be expressed as a branched covering of the n-sphere [Bull. Amer. Math. Soc. 26 (1919/20), 370–372; Jbuch 47, 529]. In general, the branch set is not a manif[...]texto impreso
If F and G are disjoint compact surfaces with boundary in S3=?D4, let F? and G? be the result of pushing F and G into the interior of D4, keeping ?F and ?G fixed. The authors give an explicit cut and paste description of an irregular 3-fold bran[...]texto impreso
The author gives a very interesting new equivalence for automorphisms u and u? of a finite-dimensional vector space E over a field K. He defines u and u? to be equivalent if there exists another automorphism H of E such that every u-invariant su[...]texto impreso
The author presents the origin of non-Euclidean geometry in the works of J. Bolyai, C. F. Gauss and N. I. Lobachevski?. The main ideas from the Appendix by Bolyai (1831) and from Pangeometria by Lobachevski? (posthumous, 1855) and the reaction o[...]texto impreso
Monzón Serrano, Juan José ; Montesinos Amilibia, José María ; Sánchez Soto, Luis Lorenzo | The Optical Society Of America | 2020-02We revisit the basic aspects of first-order optical systems from a geometrical viewpoint. In the paraxial regime, there is a wide family of beams for which the action of these systems can be represented as a Möbius transformation. We examine thi[...]texto impreso
Montesinos Amilibia, José María ; González Acuña, Francisco Javier | Canadian Mathematical Society | 1980-02-01An n-knot (Sn+2,Sn) is said to be amphicheiral if there is an orientation-reversing autohomeomorphism of Sn+2 which leaves Sn invariant as a set. An n-knot is said to be invertible if there is an orientation-preserving autohomeomorphism of Sn+2 [...]texto impreso
Montesinos Amilibia, José María ; Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa | Cambridge Univ Press | 1987-07A link or knot in S 3 is universal if it serves as common branching set for all closed, oriented 3-manifolds. A knot is simple if its exterior space is simple, i.e. any incompressible torus or annulus is parallel to the boundary. No iterated tor[...]texto impreso
For any closed orientable 3-manifold M there is a framed link (L,?) in S3 such that M is the boundary of a 4-manifold W4(L,?) obtained by adding 2-handles to the 4-ball along components of the framed link L. A link is symmetric if it is a union [...]texto impreso
Given a 3-fold simple (i.e. generic branched) covering p:M?S3, a standard modification (called "move C'' in this paper and due to the author and the reviewer in their theses in 1972) permits one to change the branch set but not the covering mani[...]texto impreso
The author starts with a discussion of various concepts of genus of a closed, orientable 3-manifold M including the well-known Heegaard genus, Hg(M), the rank, rk(M) (i.e. the minimum number of elements of ?1(M) which suffice to generate ?1(M), [...]texto impreso
Montesinos Amilibia, José María | Real Sociedad Matemática Española;Consejo Superior de Investigaciones Científicas. Instituto "Jorge Juan" de Matemáticas | 1972represented link ("nudo coloreado'') (L,?n) is a tame link L in S3 together with a transitive representation ?n of ?1(S3?L,?) into the symmetric group Sn; it can easily be pictured in the plane by a regular knot projection and a labelling of the[...]texto impreso
Applied to a knot K of S1 in S3, Zeeman's n-twist-spinning construction produces a knot Kn of S2 in S4 [ E. C. Zeeman , Trans. Amer. Math. Soc. 115 (1965), 471–495;]. Here the author gives an explicit "movie presentation'' of Kn, that is, a desc[...]texto impreso
The author describes such things as the Poincaré conjecture, Waldhausen's generalization of it, and the dimension 4 Poincaré conjecture. Then he turns to the finite-infinite and discrete-continuous dichotomies. For the former he gives examples i[...]texto impreso
The author describes such things as the Poincaré conjecture, Waldhausen's generalization of it, and the dimension 4 Poincaré conjecture. Then he turns to the finite-infinite and discrete-continuous dichotomies. For the former he gives examples i[...]texto impreso
Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | Sociedad Matemática Mexicana | 2004A link L is universal if every closed orientable 3-manifold M is a finite branched covering of S3 with the branch set equal to L. Known examples of universal links are the figure eight knot and the Borromean rings. It is also known that the tref[...]texto impreso
The main result of this paper is a new proof of a theorem which, as the author observes, is due to M. Sakuma [Math. Sem. Notes Kobe Univ. 9 (1981), no. 1, 159–180;]: For every closed, oriented, connected 3-manifold M3, there exists an Fg-bundle [...]texto impreso
We give a different proof of the result of M. Sakuma [Math. Sem. Notes Kobe Univ. 9 (1981), no. 1, 159–180] that every closed, oriented 3-manifold M has a 2-fold branched covering space N which is a surface bundle over S1. We also give a new pro[...]texto impreso
In 1969 R. P. Osborne [Fund. Math. 65 (1969), 147–151;] proved that any Cantor set in an n-manifold (open or closed) is tamely embedded in the boundary of a k-cell, for every 2?k?n. In the present work the author generalizes Osborne's result in [...]texto impreso
Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | World Scientific Publishing Co. Pte Ltd | 2016In this paper, dedicated to Prof. Lou Kauffman, we determine the Thurston’s geometry possesed by any Seifert fibered conemanifold structure in a Seifert manifold with orbit space (Formula presented.) and no more than three exceptional fibers, wh[...]texto impreso
Brumfield, G. ; Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María ; Ramírez Losada, E. ; Short, H. ; Tejada Cazorla, Juan Antonio ; Toro, M. | Sociedad Matemática Mexicana | 2008-10It has been shown [H. M. Hilden et al., Invent. Math. 87 (1987), no. 3, 441–456;] that the orbifold group U of the Borromean rings with singular angle 90 degrees is universal, i.e. for every closed orientable 3-manifold M3 there is a finite inde[...]texto impreso
Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | Cambridge Univ Press | 2006-01W. P. Thurston [Mem. Amer. Math. Soc. 59 (1986), no. 339, i–vi and 99–130;] showed that if a hyperbolic 3-manifold with b1> 1 fibers over S1, then it fibers in infinitely many different ways. In this paper, the authors consider a certain family [...]texto impreso
We introduce two notions of equivalence for rational quadratic forms. Two n-ary rational quadratic forms are commensurable if they possess commensurable groups of automorphisms up to isometry. Two n-ary rational quadratic forms F and G are proje[...]texto impreso
Montesinos Amilibia, José María ; Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa | Elsevier | 1985The authors construct a cover S3?S3 branched over the "figure eight" knot with preimage the "roman link" and a cover S3?S3 branched over the roman link with preimage containing the Borromean rings L. Since L is universal (i.e. every closed, orie[...]texto impreso
This paper deals with Heegaard splittings and Heegaard diagrams (denoted H-diagrams). Two interesting examples are given which shed light on certain questions about "minimality'' of H-diagrams. An H-diagram is a quadruple (M,F,v,w), where M is a[...]texto impreso
Two rank n, integral quadratic forms f and g are said projectively equivalent if there exist nonzero rational numbers r and s such that rf and sg are rationally equivalent. Two odd dimensional, integral quadratic forms f and g are projectivelly [...]texto impreso
Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | Graduate School of Mathematical Sciences | 1995The authors define a one-parameter family of polyhedra P(a), 0texto impreso
Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | World Scientific PublCo | 2011-10-10Representations of two bridge knot groups in the isometry group of some complete Riemannian 3-manifolds as E3 (Euclidean 3-space), H3 (hyperbolic 3-space) and E2, 1 (Minkowski 3-space), using quaternion algebra theory, are studied. We study the [...]texto impreso
Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | World Scientific PublCo | 2013-01The complete classification of representations of the Trefoil knot group G in S3 and SL(2, ?), their affine deformations, and some geometric interpretations of the results, are given. Among other results, we also obtain the classification up to [...]texto impreso
Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | World Scientific PublCo | 1995Let (p/q,n) be the 3-orbifold with base S3 and singular set the 2-bridge knot determined by the rational number p/q, with p and q odd and co-prime, and with cone angle 2?/n along the knot. In this paper the authors are interested in when the or[...]texto impreso
Groups acting properly and discontinuously on the Cartesian product (Formula presented.) of two hyperbolic planes are termed hyperabelian by Picard. The automorphism group (Formula presented.) of a quaternary integral quadratic form f of index 2[...]texto impreso
J. Birman had observed that the homological information about a given Heegaard splitting of genus g is contained in a double coset in the group of symplectic 2g×2g integer matrices with respect to a suitable subgroup, and found a determinant inv[...]texto impreso
Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | Walter de Gruyter & CO | 1992This paper continues earlier work by the authors [see, in particular, H. M. Hilden et al., Invent. Math. 87 (1987), no. 3, 441–456; H. M. Hilden, M. T. Lozano and J. M. Montesinos, in Differential topology (Siegen, 1987), 1–13, Lecture Notes in [...]texto impreso
texto impreso
Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | Sociedad Matemática Mexicana | 1992Consider the group G of a classical knot or link in S3. It is natural to consider the representations of G into PSL(2,C). The set of conjugacy classes of nonabelian representations is a closed algebraic set called the character variety (of repre[...]texto impreso
Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | Cambridge Univ Press | 2000-11A link L of the 3-sphere S3 is said to be g-periodic (g?2 an integer) if there exists an orientation preserving auto-homeomorphism h of S3 such that h(L)=L, h is of order g and the set of fixed points of h is a circle disjoint from L. A knot is [...]texto impreso
Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | Oxford University Press | 2000Given a hyperbolic knot K in S3, the SL2(C) characters of?1(S3?K) form an algebraic variety Cˆ(K). The algebraic component containing the character of the complete hyperbolic structure of S3?K is an algebraic curve CˆE(K). The desingularization [...]texto impreso
Hilden, Hugh Michael ; Montesinos Amilibia, José María ; Tejada Jiménez, Débora María ; Toro Villegas, Margarita María | Soc. Colombiana Mat. | 2012Using a new way to represent links, that we call a butter y representation, we assign to each 3-bridge link diagram a sequence of six integers,collected as a triple (p=n; q=m; s=l), such that p q s 2, 0texto impreso
A two parameter continuous family of three-dimensional Lie groups with a left invariant Riemannian metric is defined. Each of these Lie groups is the unit group of a quaternion algebra. All the possible left invariant Riemannian structures in th[...]texto impreso
Montesinos Amilibia, José María ; Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa | Springer-Verlag | 1988The authors improve the result of their previous paper on universal groups [the authors and W. Whitten, Invent. Math. 87, 411-456] and apply them to prove several interesting results on 3-manifolds. We quote some of these results below, adding n[...]texto impreso
E. C. Zeeman [Trans. Amer. Math. Soc. 115 (1965), 471–495; MR0195085 (33 #3290)] introduced the process of twist spinning a 1-knot to obtain a 2-knot (in S4), and proved that a twist-spun knot is fibered with finite cyclic structure group. R. A.[...]texto impreso
E. C. Zeeman [Trans. Amer. Math. Soc. 115 (1965), 471–495; MR0195085 (33 #3290)] introduced the process of twist spinning a 1-knot to obtain a 2-knot (in S4), and proved that a twist-spun knot is fibered with finite cyclic structure group. R. A.[...]texto impreso
Montesinos Amilibia, José María ; Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Whitten, Wilbur Carrington | Springer-Verlag | 1987Let P be a regular dodecahedron in the hyperbolic 3-space H3with the dihedral angles 90?. Choose 6 mutually disjoint edgesE1,E2,?,E6 of P such that each face of P intersects E1?E2???E6 in one edge and the opposite vertex. Let U be the group of o[...]texto impreso
Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | Hiroshima University. Faculty of Science | 2010A link in S3 is called a universal link if every closed orientable 3-manifold is a branched cover of S3 over this link. It is well known that the Borromean rings and many other links are universal links. The question whether a link is universal [...]texto impreso
Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | Graduate School of Mathematical Sciences | 1996This paper presents a technique for computing Chern-Simons invariants of certain kinds of hyperbolic 3-manifolds, namely those which are obtained as n-fold branched covers of hyperbolic knots in S3. Let S(K,?) denote the hyperbolic cone mani[...]texto impreso
This is a survey article discussing the author's work in a series of several publications on the relationship between 3-manifolds and wild knots in the 3-sphere and strings in R3 given by branched coverings. He includes an introduction to ordina[...]texto impreso
It is announced that the Freudenthal compactification of an open, connected, oriented 3-manifold is a 3-fold branched covering of S 3 . The branching set is as nice as can be expected. Some applications are given.texto impreso
It is proved that any closed orientable 3-manifold is a 3-fold irregular branched covering of the 3-sphere branched over a wildly embedded knot. These branched coverings are obtained by starting with such a branched covering over a tame knot and[...]texto impreso
Montesinos Amilibia, José María | Real Academia de Ciencias Exactas, Físicas y Naturales | 1987-01-01This is an exposition of the interrelation between orbifolds and crystallographic groups of the plane, focussing especially on patterns that occur in the Alhambra in Granada. This material appears in English in the author's book [Classical tesse[...]texto impreso
Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | Elsevier Science | 2005If K is a hyperbolic knot in S3, an algebraic component of its character variety containing one holonomy of the complete hyperbolic structure of finite volume of S3?K is an algebraic curve K. The traces of the peripheral elements of K define pol[...]texto impreso
This is a brief, elementary and nontechnical introduction to 3-dimensional topology.texto impreso
Matsumoto, Yukio ; Montesinos Amilibia, José María | Departments of Mathematics of Gakushuin University | 1991The authors prove that every geometric orbifold is good. More precisely, let X be a smooth connected manifold, and let G be a group of diffeomorphisms of X with the property that if any two elements of G agree on a nonempty open subset of X, the[...]texto impreso
The authors classify all topological types of degenerate central fibers appearing in holomorphic families of closed Riemann surfaces of genus g?2 over the unit disc. A degenerating family of genus g is a triple (M,D,?) consisting of a 2-dime[...]texto impreso
Surface mapping classes of algebraically finite type were introduced by Nielsen in 1944. Such a mapping class, in Thurston's classification, is reducible and its restriction to the reduced parts is of finite order. In the book under review, such[...]texto impreso
Montesinos Amilibia, José María ; González Acuña, Francisco Javier | European Mathematical Society | 1983A smooth n-knot K in Sn+2 is said to be quasiaspherical if Hn+1(U)=0, where U is the universal cover of the exterior of K. Let G be the group of K and H the subgroup generated by a meridian. Then (G,H) is said to be unsplittable if G does not ha[...]texto impreso
Montesinos Amilibia, José María | Real Sociedad Matemática Española;Consejo Superior de Investigaciones Científicas. Instituto "Jorge Juan" de Matemáticas | 1972Throughout his paper, the author uses "orientable manifold'' to mean a compact connected orientable 3-manifold without boundary. Such a manifold is known to be a ramified covering over a link of the 3-sphere, in which the ramification index of e[...]texto impreso
In 1920, J. W. Alexander proved that, if M3 is a closed orientable three-dimensional manifold, then there exists a covering M3?S3 that branches over a link [same Bull. 26 (1919/20), 370–372; Jbuch 47, 529]. In the paper under review, the author [...]texto impreso
Let L?S3 be a link and let t:L?S3 be its 2-fold branched cyclic cover. A represented link (L,?) is a link together with a transitive representation of ?=?1(S3?L) in Sn, the symmetric group of order n!. In his thesis ["On branched covers over a k[...]texto impreso
Let M be a closed orientable 3-manifold. A Dehn sphere S is a 2-sphere immersed in M with only double curve and triple point singularities. S fills M if S defines a cell decomposition of M. It is proven that every closed orientable 3-manifold ha[...]texto impreso
Hilden, Hugh Michael ; Montesinos Amilibia, José María ; Tejada Jiménez, Débora María ; Toro Villegas, Margarita María | Soc. Colombiana Mat. | 2005In a paper of I. V. Izmest?ev and M. Joswig [Adv. Geom. 3 (2003), no. 2, 191–225;], it was shown that any closed orientable 3-manifold M arises as a branched covering over S3 from some triangulation of S3. The proof of this result is based on th[...]texto impreso
The author shows that every compact connected oriented 3-manifold, after capping off boundary components by cones, is a covering of S3 branched over the 1-complex G which is "a pair of eyeglasses''. The author gives algorithms for passing betwee[...]texto impreso
It is a celebrated result of H. Hilden and the author of the present paper that every closed, connected, oriented 3-manifold is a 3-fold irregular (dihedral) branched covering of the 3-sphere, branched over a knot. Here the author explores a gen[...]texto impreso
If L is a link in the 3-sphere S3, let e:L˜?S3 denote the 2-fold cyclic covering of S3 branched over L. R. H. Fox [Rev. Mat. Hisp.-Amer. (4) 32 (1972), 158–166;] has shown that there is no link L in S3 such that L˜ is S1×S1×S1; the author [ibid.[...]texto impreso
From the text: "We deal with coverings of the 3-sphere S3branched over a link (= a system of knots) as a way of representing closed orientable 3-manifolds. A simplicial mapping f:Mn?Nn between two compact triangulated n-manifolds M and N is call[...]texto impreso
Montesinos Amilibia, José María ; Boileau, Michel ; González Acuña, Francisco Javier | Springer | 1987-01W. Whitten conjectured [Pacific J. Math. 97 (1981), no. 1, 209–216] that no 3-manifold obtained by a nontrivial surgery on a double of a noninvertible knot is a 2-fold branched covering of S3. The authors give counterexamples to this conjecture [...]texto impreso
The author studies the relationship between 2-fold cyclic coverings of S3 branched over a link and closed, orientable 3-manifolds that are obtained by performing surgery on a link in S3. The links of central importance are the strongly invertibl[...]texto impreso
Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | World Scientific Publishing Co | 1997The manifold M obtained by 0-surgery on the figure eight knot is a torus bundle over S1, and the core ? of the surgery is a section of the bundle. The pair (M,?) admits a structure as a hyperbolic cone-manifold with cone angle ??(0,2?). For ? of[...]texto impreso
Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | Walter de Gruyter & CO | 1992Continuing their investigation [in Topology '90 (Columbus, OH, 1990), 133–167, de Gruyter, Berlin, 1992;] of the problem of how rarely a hyperbolic orbifold is arithmetic, the authors classify the arithmetic figure eight orbifolds: there are exa[...]texto impreso
Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | Oxford University Press | 1991The Chern-Simons invariant was extended to 3-dimensional geometric cone manifolds in [H. M. Hilden, M. T. Lozano and J. M. Montesinos-Amilibia, J. Math. Sci. Univ. Tokyo 3 (1996), no. 3, 723–744; MR1432115 (98h:57056)]. The present paper is abou[...]texto impreso
H. M. Hilden [Bull. Amer. Math. Soc. 80 (1974), 1243–1244; MR0350719 (50 #3211)], U. Hirsch [Math. Z. 140 (1974), 203–230] and Montesinos [Bull. Amer. Math. Soc. 80 (1974), 845–846] showed that every closed and orientable 3-manifold is a 3-fold [...]