Algebraic and Geometric Topology 5 (2005), paper no. 57, pages 1451-1469.

Hyperbolic covering knots

Daniel S. Silver, Wilbur Whitten

Abstract. Given any knot k, there exists a hyperbolic knot tilde k with arbitrarily large volume such that the knot group pi k is a quotient of pi 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

AMS subject classification. Primary: 57M25. Secondary: 20F34.

E-print: arXiv:math.GT/0503152

DOI: 10.2140/agt.2005.5.1451

Submitted: 25 March 2005. (Revised: 4 August 2005.) Accepted: 14 September 2005. Published: 30 October 2005.

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Daniel S. Silver, Wilbur Whitten
Department of Mathematics, University of South Alabama
Mobile AL 36688, USA
1620 Cottontown Road, Forest VA 24551, USA

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