Twisted Alexander polynomials detect the unknot
arXiv:math/0604084 · doi:10.2140/agt.2006.6.1893
Abstract
The group of a nontrivial knot admits a finite permutation representation such that the corresponding twisted Alexander polynomial is not a unit.
This is the version published by Algebraic & Geometric Topology on 14 November 2006
References in corpus (2)
Cited by in corpus (9)
- Alexander invariants for virtual knots
- Twisted Alexander Polynomials and Representation Shifts
- On the tunnel number and the Morse-Novikov number of knots
- Metabelian representations, twisted Alexander polynomials, knot slicing, and mutation
- Dynamics of Twisted Alexander Invariants
- Twisted Alexander invariants detect trivial links
- Introduction to twisted Alexander polynomials and related topics
- Nontrivial Alexander polynomials of knots and links
- Non-abelian Reidemeister torsion for twist knots