Commensurability classes of twist knots

Authors

Jim Hoste, Pitzer College
Patrick D. Shanahan, Loyola Marymount UniversityFollow

Document Type

Article - post-print

Publication Date

2005

Abstract

In this paper we prove that if M_K is the complement of a non-fibered twist knot K in S³, then M_K is not commensurable to a fibered knot complement in a Z/2Z-homology sphere. To prove this result we derive a recursive description of the character variety of twist knots and then prove that a commensurability criterion developed by D. Calegari and N. Dunfield is satisfied for these varieties. In addition, we partially extend our results to a second infinite family of 2-bridge knots.

Comments

This is a post-print version of the article.

Recommended Citation

Hoste, Jim and Patrick D. Shanahan. "Commensurability classes of twist knots." Journal of Knot Theory and its Ramifications, Vol. 14, No. 1 (2005) 1-10. arXiv:math/0311051