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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 [...]texto 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
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
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
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
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
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
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
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
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
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
