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COMMENSURABILITY CLASSES OF TWIST KNOTS

JIM HOSTE

Department of Mathematics, Pitzer College, Claremont, CA 91711, USA

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and

PATRICK D. SHANAHAN

Department of Mathematics, Loyola Marymount University, Los Angeles, CA 90045, USA

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https://doi.org/10.1142/S0218216505003737Cited by:9 (Source: Crossref)

Abstract

In this paper we prove that if M_K is the complement of a non-fibered twist knot K in , 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 Calegari and Dunfield is satisfied for these varieties. In addition, we partially extend our results to a second infinite family of 2-bridge knots.

Keywords:

AMSC: 57M25

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