Publication: Hyperbolic 2-fold Branched Coverings
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Date
2001
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
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.
Description
Keywords
cyclic branched covering, hyperbolic knot, hyperbolic 3- manifold
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.