Elliptic Operators, Topology, and Asymptotic Methods (Pitman Research Notes In Mathematics Series) - Softcover

Book 13 of 39: Chapman & Hall/CRC Research Notes in Mathematics

Roe, John

 
9780582325029: Elliptic Operators, Topology, and Asymptotic Methods (Pitman Research Notes In Mathematics Series)
Softcover
ISBN 10: 0582325021 ISBN 13: 9780582325029
Publisher: Chapman and Hall/CRC, 1999

Synopsis

This Research Note gives an introduction to the circle of ideas surrounding the `heat equation proof' of the Atiyah-Singer index theorem. Asymptotic expansions for the solutions of partial differential equations on compact manifolds are used to obtain topological information, by means of a `supersymmetric' cancellation of eigenspaces. The analysis is worked out in the context of Dirac operators on Clifford bundles.

The work includes proofs of the Hodge theorem; eigenvalue estimates; the Lefschetz theorem; the index theorem; and the Morse inequalities. Examples illustrate the general theory, and several recent results are included.

This new edition has been revised to streamline some of the analysis and to give better coverage of important examples and applications.

Readership: The book is aimed at researchers and graduate students with a background in differential geometry and functional analysis.

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

About the Author

John Roe

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

Publisher
Chapman and Hall/CRC
Publication date
1999
Language
English
ISBN 10 
0582325021
ISBN 13 
9780582325029
Binding
Paperback
Edition number
2
Number of pages
220

Other Popular Editions of the Same Title

9781138417670: Elliptic Operators, Topology, and Asymptotic Methods (Chapman & Hall/CRC Research Notes in Mathematics Series)

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ISBN 10:  113841767X ISBN 13:  9781138417670
Publisher: Chapman and Hall/CRC, 2017
Hardcover