Algebraic & Geometric Topology Volume 6, issue 4 (2006)

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Twisted Alexander polynomials detect the unknot

Daniel S Silver and Susan G Williams

Algebraic & Geometric Topology 6 (2006) 1893–1901

DOI: 10.2140/agt.2006.6.1893

arXiv: math.GT/0604084

Abstract

The group of a nontrivial knot admits a finite permutation representation such that the corresponding twisted Alexander polynomial is not a unit.

Keywords

knot, Alexander polynomial, twisted Alexander polynomial.

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 37B40

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Publication

Received: 5 June 2006

Revised: 20 August 2006

Accepted: 11 September 2006

Published: 14 November 2006

Authors

Daniel S Silver
Department of Mathematics and Statistics University of South Alabama Mobile, AL 36688-0002 USA

Susan G Williams
Department of Mathematics and Statistics University of South Alabama Mobile, AL 36688-0002 USA