CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Twisted Alexander Invariants Detect Trivial Links

  Published:2017-02-21
 Printed: Jun 2017
  • Stefan Friedl,
    Fakultät für Mathematik, Universität Regensburg, Germany
  • Stefano Vidussi,
    Department of Mathematics, University of California, Riverside, CA 92521, USA
Format:   LaTeX   MathJax   PDF  

Abstract

It follows from earlier work of Silver--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: twisted Alexander polynomial, virtual fibering theorem, unlink detection twisted Alexander polynomial, virtual fibering theorem, unlink detection
MSC Classifications: 57M27 show english descriptions Invariants of knots and 3-manifolds 57M27 - Invariants of knots and 3-manifolds
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/