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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[...]
