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Laplacian on a Riemannian Manifold: An Introduction to Analysis on Manifolds

Laplacian on a Riemannian Manifold: An Introduction to Analysis on Manifolds

by Rosenberg, S
No customer reviews yet ISBN 9780521463003 Cambridge University Press

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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BrandCambridge University Press
Pub dateJan 9, 1997
ISBN-100521463009
ISBN-139780521463003
Hardcover188.0 pages
LanguageEnglish
Dimensions9.25 × 0.5 × 6.25 in
Weight1 lb
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