Commensurability classes of twist knots

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Abstract

In this paper we prove that if M K is the complement of a non-fibered twist knot K in S 3 , 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.

Original languageAmerican English
Pages (from-to)1-10
JournalJournal of Knot Theory and its Ramifications
Volume14
Issue number1
StatePublished - 2005

Keywords

  • Geometric topology
  • knot theory
  • hyperbolic geometry

Disciplines

  • Geometry and Topology

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