## Algebraic & Geometric Topology

### Twisted Alexander polynomials detect the unknot

#### Abstract

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

#### Article information

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

Dates
Revised: 20 August 2006
Accepted: 11 September 2006
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796609

Digital Object Identifier
doi:10.2140/agt.2006.6.1893

Mathematical Reviews number (MathSciNet)
MR2263053

Zentralblatt MATH identifier
1132.57010

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

#### Citation

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. https://projecteuclid.org/euclid.agt/1513796609

#### References

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