Commensurability classes of twist knots

Details Commensurability classes of twist knots Commensurability classes of twist knots

2003-11-05

arxiv.org/abs/math/0311051v2

J. Knot Theory and its Ramifications 14.1 (2005) 91-100

Mathematics

Geometric Topology

10 pages, 3 figures

Scientific paper

In this paper we prove that if $M_K$ is the complement of a non-fibered twist knot $K$ in $\mathbb S^3$, then $M_K$ is not commensurable to a fibered knot complement in a $\mathbb Z/ 2 \mathbb Z$-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.

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