Geometry & Topology 16 (2012) 625–664

DOI: 10.2140/gt.2012.16.625

Abstract

We investigate commensurability classes of hyperbolic knot complements in the generic case of knots without hidden symmetries. We show that such knot complements which are commensurable are cyclically commensurable, and that there are at most 3 hyperbolic knot complements in a cyclic commensurability class. Moreover if two hyperbolic knots have cyclically commensurable complements, then they are fibred with the same genus and are chiral. A characterization of cyclic commensurability classes of complements of periodic knots is also given. In the nonperiodic case, we reduce the characterization of cyclic commensurability classes to a generalization of the Berge conjecture.

Keywords

hyperbolic knot, commensurability

Mathematical Subject Classification

Primary: 57M10, 57M25

References

Publication

Received: 8 February 2011
Accepted: 27 November 2011
Published: 18 April 2012
Proposed: Cameron Gordon
Seconded: Walter Neumann, Colin Rourke

Authors