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 Müller 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.

pages 29, final version, to appear in "The Legacy of Bernhard Riemann After One Hundred and Fifty Years" , Advanced Lectures in Mathematics 35, Higher Education Press, Bejing

References in corpus (1)

• Generalized holomorphic analytic torsion

Cited by in corpus (2)

• Rank, combinatorial cost and homology torsion growth in higher rank lattices
• Harmonic Forms, Minimal Surfaces and Norms on Cohomology of Hyperbolic $3$-Manifolds