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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