Algebraic & Geometric Topology

Twisted Alexander polynomials detect the unknot

Daniel S Silver and Susan G Williams

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

Article information

Algebr. Geom. Topol., Volume 6, Number 4 (2006), 1893-1901.

Received: 5 June 2006
Revised: 20 August 2006
Accepted: 11 September 2006
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 37B40: Topological entropy

knot Alexander polynomial twisted Alexander polynomial.


Silver, Daniel S; Williams, Susan G. Twisted Alexander polynomials detect the unknot. Algebr. Geom. Topol. 6 (2006), no. 4, 1893--1901. doi:10.2140/agt.2006.6.1893.

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