Volume 8, issue 2 (2008)

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Commensurability classes of $2$–bridge knot complements

Alan W Reid and Genevieve S Walsh

Algebraic & Geometric Topology 8 (2008) 1031–1057
Abstract

We show that a hyperbolic 2–bridge knot complement is the unique knot complement in its commensurability class. We also discuss constructions of commensurable hyperbolic knot complements and put forth a conjecture on the number of hyperbolic knot complements in a commensurability class.

Keywords
commensurability, hyperbolic knot complement, 2-bridge knot
Mathematical Subject Classification 2000
Primary: 57M25, 57M10
Secondary: 57M27
References
Publication
Received: 8 January 2008
Revised: 22 May 2008
Accepted: 2 June 2008
Published: 5 July 2008
Authors
Alan W Reid
Department of Mathematics
University of Texas
Austin, TX 78712
USA
http://www.ma.utexas.edu/users/areid/
Genevieve S Walsh
Department of Mathematics
Tufts University
Medford, MA 02155
USA
http://www.tufts.edu/~gwalsh01/