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TWISTED ALEXANDER POLYNOMIALS OF 2-BRIDGE KNOTS

JIM HOSTE

Pitzer College, 1050 N. Mills Ave, Claremont CA 91711, USA

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and

PATRICK D. SHANAHAN

Department of Mathematics, Loyola Marymount University, 1 LMU Drive, Los Angeles CA 90045, USA

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https://doi.org/10.1142/S0218216512501386Cited by:6 (Source: Crossref)

Abstract

We investigate the twisted Alexander polynomial of a 2-bridge knot associated to a Fox coloring. For several families of 2-bridge knots, including but not limited to, torus knots and genus-one knots, we derive formulae for these twisted Alexander polynomials. We use these formulae to confirm a conjecture of Hirasawa and Murasugi for these knots.

Keywords:

AMSC: 57M25

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