Volume 8, issue 3 (2008)

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Commensurability classes of $(-2,3,n)$ pretzel knot complements

Melissa L Macasieb and Thomas W Mattman

Algebraic & Geometric Topology 8 (2008) 1833–1853
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 n7, 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 2000
Primary: 57M25
References
Publication
Received: 2 April 2008
Revised: 17 July 2008
Accepted: 22 August 2008
Published: 20 October 2008
Authors
Melissa L Macasieb
Department of Mathematics
The University of British Columbia
Room 121, 1984 Mathematics Road
Vancouver, BC V6T 1Z2
Canada
Thomas W Mattman
Department of Mathematics and Statistics
California State University, Chico
Chico, CA 95929-0525
USA