Commensurability classes of 2–bridge knot complements

Reid, Alan W; Walsh, Genevieve S

doi:10.2140/agt.2008.8.1031

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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

DOI: 10.2140/agt.2008.8.1031

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/

Volume 8, issue 2 (2008)