Publication: Around the Borromean link
No Thumbnail Available
Full text at PDC
Publication Date
2008-03
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Citations
Exportar
Abstract
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 group
Description
UCM subjects
Unesco subjects
Keywords
Citation
Armstrong, M. A., (1968). The fundamental group of the orbit space of a discontinuous group. Proc. Cambridge Philos. Soc., 64, 299–301.
Cromwell, Peter, Beltrami, Elisabetta and Rampichini, Marta, (1998). The Borromean rings, Math. Intelligencer, 20, 1, 53–62.
Fox, R.-H., (1962). A quick trip through knot theory. Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961), 120–167, Prentice-Hall, Englewood Cliffs, N.J.55.20
Hilden, Hugh M., Lozano, M. T. and Montesinos, José María, (1983). Universal knots. Bull. Amer. Math. Soc., (N.S.), 8, 3, 449–450.
Hilden, Hugh M., Lozano, María Teresa and Montesinos, José María, Universal knots. Knot theory and manifolds (Vancouver, B.C., 1983), 25–59, Lecture Notes in Math., 1144, Springer, Berlin, 1985.
Hilden, Hugh M., Lozano, María Teresa and Montesinos, José María, (1983). The Whitehead link, the Borromean rings and the knot 946 are universal. Collect. Math., 34, 1, 19–28.
Hilden, Hugh M., Lozano, Maria Teresa and Montesinos, José María, (1985). On knots that are universal. Topology, 24, 4, 499–504.
Hilden, H. M., Lozano, M. T., Montesinos, J. M. and Whitten, W. C., (1987). On universal groups and three-manifolds, Invent. Math., 87, 3, 441–456.
Hilden, Hugh M., Lozano, María Teresa and Montesinos, José María, (1988). On the universal group of the Borromean rings, Differential topology (Siegen, 1987), 1–13, Lecture Notes in Math., 1350, Springer, Berlin, 1988.
Hilden, Hugh M., Lozano, María Teresa and Montesinos-Amilibia, José María, On the Borromean orbifolds: geometry and arithmetic. Topology '90 (Columbus, OH, 1990), 133–167, Ohio State Univ. Math. Res. Inst. Publ., 1, de Gruyter, Berlin, 1992. (Reviewer: B. N. Apanasov)
Hilden, Hugh M., Lozano, María Teresa and Montesinos-Amilibia, José María, (1993). Universal 2-bridge knot and link orbifolds. J. Knot Theory Ramifications, 2, 2, 141–148.
Hilden, Hugh M., Lozano, María Teresa and Montesinos-Amilibia, José María, (2001). The arithmetic structure of a universal group. Dedicated to the memory of Professor M. Pezzana (Italian). Atti Sem. Mat. Fis. Univ. Modena, 49, suppl., 1–14.
Hilden, Hugh M., Lozano, María Teresa and Montesinos-Amilibia, José María, (2004). On 2-universal knots. Bol. Soc. Mat. Mexicana (3), 10, Special Issue, 239–253.
Hilden, Hugh M., Lozano, María Teresa and Montesinos-Amilibia, José María, (2006). On hyperbolic 3-manifolds with an infinite number of fibrations over S1, Math. Proc. Cambridge Philos. Soc., 140, 1, 79–93.
Jones, Kerry N., (1994). The structure of closed non-positively curved Euclidean cone 3-manifolds. Pacific J. Math., 163, 2, 297–313.
Jones, Kerry N., (1994). Geometric structures on branched covers over universal links. Geometric topology (Haifa, 1992), 47–58, Contemp. Math., 164, Amer. Math. Soc., Providence, RI.
Lozano, María Teresa and Montesinos-Amilibia, José María, (1997). Geodesic flows on hyperbolic orbifolds, and universal orbifolds. Pacific J. Math., 177, 1, 109–147.
Maclachlan, Colin and Reid, Alan W. The arithmetic of hyperbolic 3-manifolds, Graduate Texts in Mathematics, 219, Springer-Verlag, New York, 2003. xiv+463
Matsumoto, K., (2006). Automorphic functions with respect to the fundamental group of the complement of the Borromean rings, J. Math. Sci. Univ. Tokyo, 13, 1, 1–11.
Matsumoto, Yukio and Montesinos-Amilibia, José María, (1991). A proof of Thurston's uniformization theorem of geometric orbifolds. Tokyo J. Math., 14, 1, 181–196.
Montesinos, José María, (1983). Representing 3-manifolds by a universal branching set. Math. Proc. Cambridge Philos. Soc., 94, 1, 109–123.
Ramirez, Arturo, (1975). On a theorem of Alexander, (Spanish), An. Inst. Mat. Univ. Nac. Autónoma México, 15, 1, 77–81.
Ratcliffe, John G., (2006). Foundations of hyperbolic manifolds. Second edition. Graduate Texts in Mathematics, 149, Springer, New York, xii+779.
Rolfsen, Dale, (1990). Knots and links, Corrected reprint of the 1976 original. Mathematics Lecture Series, 7, Publish or Perish, Inc., Houston, TX, xiv+439 pp.
Toda, Masahito, (2004). Representation of finite groups and the first Betti number of branched coverings of a universal Borromean orbifold, Cent. Eur. J. Math., 2, 2, 218–249 (electronic).
Thurston, William P., Three-dimensional geometry and topology, Vol. 1. Edited by Silvio Levy. Princeton Mathematical Series, 35, Princeton University Press, Princeton, NJ, 1997. x+311 pp.
Uchida, Yoshiaki, (1992). Universal pretzel links. Knots 90, (Osaka, 1990), 241–270, de Gruyter, Berlin.
Uchida, Yoshiaki, (1991). Universal chains, Kobe J. Math., 8, 1, 55–65.