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.
CITATION STYLE
Friedl, S., & Vidussi, S. (2011). A Survey of Twisted Alexander Polynomials. In The Mathematics of Knots (pp. 45–94). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-15637-3_3
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