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Autor Hilden, Hugh Michael |
Documentos disponibles escritos por este autor (38)
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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[...]