On \pi-hyperbolic knots with the same 2-fold branched coverings |
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Authors: | Marco Reni |
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Institution: | (1) Università degli Studi di Trieste, Dipartimento di Scienze Matematiche, Piazzale Europa, 1, 34100 Trieste, Italy (e-mail: reni@univ.trieste.it) , IT |
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Abstract: | We consider the following problem from the Kirby's list (Problem 3.25): Let K be a knot in and M(K) its 2-fold branched covering space. Describe the equivalence class K] of K in the set of knots under the equivalence relation if is homeomorphic to . It is known that there exist arbitrarily many different hyperbolic knots with the same 2-fold branched coverings, due to
mutation along Conway spheres. Thus the most basic class of knots to investigate are knots which do not admit Conway spheres.
In this paper we solve the above problem for knots which do not admit Conway spheres, in the following sense: we give upper
bounds for the number of knots in the equivalence class K] of a knot K and we describe how the different knots in the equivalence class of K are related.
Received: 3 August 1998 / in final form: 17 June 1999 |
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Keywords: | Mathematics Subject Classification (1991):57M12 57M25 57M50 |
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