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The Laplacian on a Riemannian Manifold : An Introduction to Analysis on Manifolds - Steven Rosenberg

The Laplacian on a Riemannian Manifold

An Introduction to Analysis on Manifolds

By: Steven Rosenberg, J. Bruce (Editor)

Hardcover

Published: 27th May 2006
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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.

"The book is well written... This book provides a very readable introduction to heat kernal methods and it can be strongly recommended for graduate students of mathematics looking for a thorough introduction to the topic." Friedbert PrUfer, Mathematical Reviews

Introduction
The Laplacian on a Riemannian manifold
Elements of differential geometry
The construction of the heat kernel
The heat equation approach to the Atiyah-Singer index theorem
Zeta functions of Laplacians
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521463003
ISBN-10: 0521463009
Series: London Mathematical Society Student Texts
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 188
Published: 27th May 2006
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 1.4
Weight (kg): 0.45