An introduction to the abelian Reidemeister torsion of three-dimensional manifolds

TL;DR

This paper introduces the abelian Reidemeister torsion for 3-manifolds, discusses its refinements, and surveys its applications and relations to other classical invariants, providing foundational knowledge for topologists.

Contribution

It offers an accessible introduction to Reidemeister torsion and its refinements, highlighting their applications in 3-manifold topology.

Findings

Reidemeister torsion relates to classical invariants

Refinements by Turaev enhance the torsion's applications

Applications include connections to other topological invariants

Abstract

These notes accompany some lectures given at the autumn school "Tresses in Pau" in October 2009. The abelian Reidemeister torsion for 3-manifolds, and its refinements by Turaev, are introduced. Some applications, including relations between the Reidemeister torsion and other classical invariants, are surveyed.