The Laplacian on a Riemannian Manifold: An Introduction to Analysis on Manifolds (London Mathematical Society Student Texts, Series Number 31) (Volume 0) - Softcover

Book 25 of 83: London Mathematical Society Student Texts

Rosenberg, Steven

 
9780521468312: The Laplacian on a Riemannian Manifold: An Introduction to Analysis on Manifolds (London Mathematical Society Student Texts, Series Number 31) (Volume 0)
Softcover
ISBN 10: 0521468310 ISBN 13: 9780521468312
Publisher: Cambridge University Press, 1997

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.

"synopsis" may belong to another edition of this title.

Book Description

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. 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.

Review

"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 PrÜfer, Mathematical Reviews

"About this title" may belong to another edition of this title.

Publisher
Cambridge University Press
Publication date
1997
Language
English
ISBN 10 
0521468310
ISBN 13 
9780521468312
Binding
Paperback
Edition number
1
Number of pages
188

Other Popular Editions of the Same Title

9780521463003: The Laplacian on a Riemannian Manifold: An Introduction to Analysis on Manifolds (London Mathematical Society Student Texts, Series Number 31)

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ISBN 10:  0521463009 ISBN 13:  9780521463003
Publisher: Cambridge University Press, 1997
Hardcover