Twisted Alexander polynomials of 2-bridge knots

Authors

Jim Hoste, Pitzer College
Patrick D. Shanahan, Loyola Marymount UniversityFollow

Document Type

Article - post-print

Publication Date

2013

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.

Comments

This article is the post-print version.

Recommended Citation

Hoste, Jim and Patrick Shanahan. "Twisted Alexander polynomials of 2-bridge knots." Journal of Knot Theory and its Ramifications, Vol. 22, No. 1 (2013) 1-29. arXiv:1206.1894.