A survey of twisted Alexander polynomials
Stefan Friedl, Stefano Vidussi

TL;DR
This paper surveys the theory of twisted Alexander polynomials for 3-manifolds, discussing their properties, relation to Reidemeister torsion, and applications in topology, including higher order variants.
Contribution
It provides a comprehensive overview of twisted Alexander polynomials, highlighting their formal properties, relationships, and diverse applications in topological research.
Findings
Summarizes formal properties of twisted Alexander polynomials
Explains their relationship to twisted Reidemeister torsion
Reviews applications to topological problems
Abstract
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology
