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Autor Hilden, Hugh Michael |
Documentos disponibles escritos por este autor (38)
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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 [...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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 [...]![]()
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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[...]![]()
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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), 0![]()
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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 [...]![]()
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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 [...]![]()
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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[...]![]()
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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 [...]![]()
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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[...]![]()
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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 [...]![]()
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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 [...]![]()
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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, 0![]()
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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[...]![]()
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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[...]![]()
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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 [...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | Springer | 1983W. Thurston proved the existence of universal links L?S3 which are defined by the property that every closed orientable 3-manifold is a branched covering over L?S3. The authors answered earlier [Bull. Amer. Math. Soc. (N.S.) 8 (1983), no. 3, 449[...]![]()
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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 | 2008-10A finite covolume, discrete group of hyperbolic isometries U, acting on H3, is said to be universal if for every closed orientable 3-manifold M3 there is a finite index subgroup G of U so that M3=H3/G. It has been shown [H. M. Hilden et al., Inv[...]![]()
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Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | World Scientific PublCo | 1993Let (L,n) be the orbifold with singular set a nontoroidal 2-bridge knot or link L in S3, with cyclic isotropy group of order n. The authors show that the orbifold fundamental group ?=?1(L,12n) is universal: ? is isomorphic to a discrete group of[...]![]()
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Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | Springe | 1985This paper contains detailed proofs of the results in the announcement "Universal knots'' [the authors, Bull. Amer. Math. Soc. (N.S.) 8 (1983), 449–450;]. The authors exhibit a knot K that is universal, i.e. every closed, orientable 3-manifold M[...]![]()
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Montesinos Amilibia, José María ; Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa | American Mathematical Society | 1983In an unpublished preprint W. Thurston showed the existence of a six component link in the 3-sphere such that every three-manifold can be expressed as a branched cover of the 3-sphere branched over this link. He called links with this property "[...]![]()
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Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María | World Scientific Publishing Co., Inc | 1996In this paper, the authors compute the volumes and Chern-Simons invariants for a class of hyperbolic 3-manifolds, namely, the n-fold branched covers of S3 along the 2-bridge knots p/q. The computation is based on the formula of Schläffli. In a 1[...]