The Atiyah-Patodi-Singer Index Theorem

by Richard Melrose

Overview

Based on the lecture notes of a graduate course given at MIT, this sophisticated treatment leads to a variety of current research topics and will undoubtedly serve as a guide to further studies.

Product Details

ISBN-13:	9781040187814
Publisher:	CRC Press
Publication date:	03/31/1993
Series:	Research Notes in Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	392
File size:	1 MB

Table of Contents

Introduction and the proof 1 Ordinary differential problems 2 Exact b-geometry 3 Spin Structures 4 Small b-calculus 5 Full calculus 6 Relative index, cohomology and resolvent 7 Heat calculus 8 Local index theorem 9 Proof revisited and applications.

Editorial Reviews

Places the A-P-S index theorem in an analytic framework analogous to that provided by the theory of pseudodifferential operators for the A-S theorem. The A-P-S theorem is used to discuss some important aspects of geometry and analysis on manifolds with boundary. The author begins by stating and proving the theorem, then uses the remaining chapters to flesh out these initial concepts. An introduction to the "b" category and the related calculus of b-pseudodifferential operators on boundaried compact manifolds is given. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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