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Hyperbolic covering knots

Daniel S Silver and Wilbur Whitten

Algebraic & Geometric Topology 5 (2005) 1451–1469

arXiv: math.GT/0503152

Abstract

Given any knot k, there exists a hyperbolic knot k̃ with arbitrarily large volume such that the knot group πk is a quotient of πk̃ by a map that sends meridian to meridian and longitude to longitude. The knot k̃ can be chosen to be ribbon concordant to k and also to have the same Alexander invariant as k.

Keywords
Alexander module, hyperbolic knot, ribbon concordance, tangle
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 20F34
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Publication
Received: 25 March 2005
Revised: 4 August 2005
Accepted: 14 September 2005
Published: 30 October 2005
Authors
Daniel S Silver
Department of Mathematics
University of South Alabama
Mobile AL 36688
USA
Wilbur Whitten
1620 Cottontown Road
Forest VA 24551
USA