Survey on analytic and topological torsion

Abstract

The article consists of a survey on analytic and topological torsion. Analytic torsion is defined in terms of the spectrum of the analytic Laplace operator on a Riemannian manifold, whereas topological torsion is defined in terms of a triangulation. The celebrated theorem of Cheeger and M\"uller identifies these two notions for closed Riemannian manifolds. We also deal with manifolds with boundary and with isometric actions of finite groups. The basic theme is to extract topological invariants from the spectrum of the analytic Laplace operator on a Riemannian manifold.