Twisted Alexander polynomials of periodic knots

Details Twisted Alexander polynomials of periodic knots Twisted Alexander polynomials of periodic knots

2004-12-19

arxiv.org/abs/math/0412380v3

Algebr. Geom. Topol. 6 (2006) 145-169

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 24 February 2006

Scientific paper

10.2140/agt.2006.6.145

Murasugi discovered two criteria that must be satisfied by the Alexander polynomial of a periodic knot. We generalize these to the case of twisted Alexander polynomials. Examples demonstrate the application of these new criteria, including to knots with trivial Alexander polynomial, such as the two polynomial 1 knots with 11 crossings. Hartley found a restrictive condition satisfied by the Alexander polynomial of any freely periodic knot. We generalize this result to the twisted Alexander polynomial and illustrate the applicability of this extension in cases in which Hartley's criterion does not apply.

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