Algebraic & Geometric Topology 8 (2008) 1833–1853

DOI: 10.2140/agt.2008.8.1833

Abstract

Let K be a hyperbolic (−2,3,n) pretzel knot and M = S³ ∖ K its complement. For these knots, we verify a conjecture of Reid and Walsh: there are at most three knot complements in the commensurability class of M. Indeed, if n≠7, we show that M is the unique knot complement in its class. We include examples to illustrate how our methods apply to a broad class of Montesinos knots.

Keywords

commensurability class, pretzel knot, trace field

Mathematical Subject Classification

Primary: 57M25

References

Publication

Received: 2 April 2008
Revised: 17 July 2008
Accepted: 22 August 2008
Published: 20 October 2008

Authors