Twisted Alexander polynomials detect the unknot

Daniel S Silver; Susan G Williams

doi:10.2140/agt.2006.6.1893

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Home > Journals > Algebr. Geom. Topol. > Volume 6 > Issue 4 > Article

2006 Twisted Alexander polynomials detect the unknot

Daniel S Silver, Susan G Williams

Algebr. Geom. Topol. 6(4): 1893-1901 (2006). DOI: 10.2140/agt.2006.6.1893

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Abstract

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

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Daniel S Silver. Susan G Williams. "Twisted Alexander polynomials detect the unknot." Algebr. Geom. Topol. 6 (4) 1893 - 1901, 2006. https://doi.org/10.2140/agt.2006.6.1893

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Received: 5 June 2006; Revised: 20 August 2006; Accepted: 11 September 2006; Published: 2006

First available in Project Euclid: 20 December 2017

zbMATH: 1132.57010

MathSciNet: MR2263053

Digital Object Identifier: 10.2140/agt.2006.6.1893

Subjects:

Primary: 57M25

Secondary: 37B40

Keywords: Alexander polynomial , knot , twisted Alexander polynomial.

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Daniel S Silver, Susan G Williams "Twisted Alexander polynomials detect the unknot," Algebraic & Geometric Topology, Algebr. Geom. Topol. 6(4), 1893-1901, (2006)

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