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Article
Commensurability classes of twist knots
Journal of Knot Theory and its Ramifications
  • Jim Hoste, Pitzer College
  • Patrick D. Shanahan, Loyola Marymount University
Document Type
Article - post-print
Publication Date
1-1-2005
Disciplines
Abstract
In this paper we prove that if MK is the complement of a non-fibered twist knot K in S3, then MK 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.

Citation Information
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