✦ LIBER ✦

The Laplacian on a Riemannian manifold

✍ Scribed by Steven Rosenberg

Book ID: 127436545
Publisher: Cambridge University Press
Year: 1997
Tongue: English
Weight: 5 MB
Series: London Mathematical Society Student Texts
Category: Library
ISBN: 0521468310

No coin nor oath required. For personal study only.

✦ Synopsis

This text on analysis on Riemannian manifolds is a thorough introduction to topics covered in advanced research monographs on Atiyah-Singer index theory. The main theme is the study of heat flow associated to the Laplacians on differential forms. This provides a unified treatment of Hodge theory and the supersymmetric proof of the Chern-Gauss-Bonnet theorem. In particular, there is a careful treatment of the heat kernel for the Laplacian on functions. The author develops the Atiyah-Singer index theorem and its applications (without complete proofs) via the heat equation method. Rosenberg also treats zeta functions for Laplacians and analytic torsion, and lays out the recently uncovered relation between index theory and analytic torsion. The text is aimed at students who have had a first course in differentiable manifolds, and the author develops the Riemannian geometry used from the beginning. There are over 100 exercises with hints.

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