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This text on analysis of 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 Atiyah-Singer index theorem and its applications are developed (without complete proofs) via the heat equation method. Zeta functions for Laplacians and analytic torsion are also treated, and the recently uncovered relation between index theory and analytic torsion is laid out. The text is aimed at students who have had a first course in differentiable manifolds, and the Riemannian geometry used is developed from the beginning. There are over 100 exercises with hints.

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Book Details

ISBN: 9780521468312
ISBN-10: 0521468310
Format: Paperback
(228mm x 152mm x 11mm)
Pages: 188
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 9-Jan-1997
Country of Publication: United Kingdom

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Books By Author Steven Rosenberg

Laplacian on a Riemannian Manifold by Steven Rosenberg

The Laplacian on a Riemannian Manifold

Hardback, January 1997
$220.50