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Twisted Alexander Invariants Detect Trivial Links

Friedl, Stefan and Vidussi, Stefano (2017) Twisted Alexander Invariants Detect Trivial Links. Canadian Mathematical Bulletin 60 (02), pp. 283-299.

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Other URL: http://doi.org/10.4153/CMB-2016-097-x


Abstract

It follows from earlier work of Silver and Williams and the authors that twisted Alexander polynomials detect the unknot and the Hopflink. 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.


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Item type:Article
Date:2017
Institutions:Mathematics > Prof. Dr. Stefan Friedl
Identification Number:
ValueType
10.4153/CMB-2016-097-xDOI
Keywords:THURSTON NORM; REIDEMEISTER TORSION; FIBERED MANIFOLDS; GRAPH MANIFOLDS; FLOER HOMOLOGY; POLYNOMIALS; KNOTS; twisted Alexander polynomial; virtual fibering theorem; unlink detection
Dewey Decimal Classification:500 Science > 510 Mathematics
Status:Published
Refereed:Yes, this version has been refereed
Created at the University of Regensburg:Yes
Item ID:38952
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