Hyperbolic covering knots

Silver, Daniel S; Whitten, Wilbur

doi:10.2140/agt.2005.5.1451

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Hyperbolic covering knots

Daniel S Silver and Wilbur Whitten

Algebraic & Geometric Topology 5 (2005) 1451–1469

DOI: 10.2140/agt.2005.5.1451

arXiv: math.GT/0503152

Abstract

Given any knot $k$ , there exists a hyperbolic knot $\tilde{k}$ with arbitrarily large volume such that the knot group $π k$ is a quotient of $π \tilde{k}$ by a map that sends meridian to meridian and longitude to longitude. The knot $\tilde{k}$ 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

Volume 5, issue 4 (2005)