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Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4241

Title: Hyperbolic 2-fold Branched Coverings
Authors: Mecchia, Mattia
Keywords: cyclic branched covering
hyperbolic knot
hyperbolic 3- manifold
Issue Date: 2001
Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Citation: Mattia Mecchia, "Hyperbolic 2-fold Branched Coverings", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 32 (2001) suppl.1, pp. 165–180.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
32 suppl. 1 (2001)
Abstract: In the Kirby list is presented the following problem: describe the equivalence classes in the set of knots under the relation K$_{1}$ is equivalent to K$_{2}$ if their 2-fold cyclic branched coverings are homeomorphic 3-manifolds. In this paper we consider the basic case of hyperbolic manifold. In the fi{}rst part of this paper we want to present briefl{}y the results, yet available in some previous works, which solve this problem. In the second part we present examples of knots with the same 2-fold branched covering which show that the theorem, which describes the possible relations between two knots in the same equivalence class, is the best possible.
URI: http://hdl.handle.net/10077/4241
ISSN: 0049-4704
MS Classification: 57M12
57M25
57M50
Appears in Collections:Rendiconti dell‘ Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.32 (2001) s1

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