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Twisted Alexander Invariants Detect Trivial Links

Published online by Cambridge University Press:  20 November 2018

Stefan Friedl  and
Stefano Vidussi
Stefan Friedl
Affiliation:
Fakultät für Mathematik, Universität Regensburg, Germany. e-mail: sfriedl@gmail.com
Stefano Vidussi
Affiliation:
Department of Mathematics, University of California, Riverside, CA 92521, USA. e-mail: svidussi@math.ucr.edu
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Abstract

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It follows from earlier work of Silver and Williams and the authors that twisted Alexander polynomials detect the unknot and the Hopf link. We now show that twisted Alexander polynomials also detect the trefoil and the figure-8 knot, that twisted Alexander polynomials detect whether a link is split and that twisted Alexander modules detect trivial links. We use this result to provide algorithms for detecting whether a link is the unlink, whether it is split, and whether it is totally split.

Keywords

57M27twisted Alexander polynomialvirtual fibering theoremunlink detection
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 2 , 01 June 2017 , pp. 283 - 299
Copyright
Copyright © Canadian Mathematical Society 2017

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