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2006 Twisted Alexander polynomials of periodic knots
Jonathan A Hillman, Charles Livingston, Swatee Naik
Algebr. Geom. Topol. 6(1): 145-169 (2006). DOI: 10.2140/agt.2006.6.145

Abstract

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.

Citation

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Jonathan A Hillman. Charles Livingston. Swatee Naik. "Twisted Alexander polynomials of periodic knots." Algebr. Geom. Topol. 6 (1) 145 - 169, 2006. https://doi.org/10.2140/agt.2006.6.145

Information

Received: 17 June 2005; Revised: 24 January 2006; Accepted: 26 January 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1097.57010
MathSciNet: MR2199457
Digital Object Identifier: 10.2140/agt.2006.6.145

Subjects:
Primary: 57M25, 57M27

Rights: Copyright © 2006 Mathematical Sciences Publishers

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