Stefan Friedl, Stefano Vidussi
Published 2009-05-05, updated 2010-02-05Version 3
We give a short introduction to the theory of twisted Alexander polynomials of a 3--manifold associated to a representation of its fundamental group. We summarize their formal properties and we explain their relationship to twisted Reidemeister torsion. We then give a survey of the many applications of twisted invariants to the study of topological problems. We conclude with a short summary of the theory of higher order Alexander polynomials.
Comments: 42 pages, final version of the survey paper to be published by the proceedings of the conference `The Mathematics of Knots: Theory and Application' in Heidelberg in December 2008. In the final version we updated references and fixed a few typos
Metabelian representations, twisted Alexander polynomials, knot slicing, and mutation
n-Quasi-isotopy: I. Questions of nilpotence
The parity of the Cochran-Harvey invariants of 3-manifolds
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