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Global Analysis on Foliated Spaces

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Synopses & Reviews

Publisher Comments:

Foliated spaces look locally like products, but their global structure is generally not a product, and tangential differential operators are correspondingly more complex. In the 1980s, Alain Connes founded what is now known as noncommutative geometry. One of the first results was his generalization of the Atiyah-Singer index theorem to compute the analytic index associated with a tangential (pseudo)-differential operator and an invariant transverse measure on a foliated manifold, in terms of topological data on the manifold and the operator. This book presents a complete proof of this beautiful result, generalized to foliated spaces (not just manifolds).

Book News Annotation:

The first edition was published in 1988, and much has happened in the field since then. This second edition is adds updates at the end of each chapter, a new appendix reprinting a relevant article from Mathematical Reviews, an enlarged bibliography, and an index. Mathematicians Moore (U. of California-Berkeley) and Schochet (Wayne State U.) based this work on their lecture notes to serve as an introduction to the field and as a reference for students and researchers. In it they develop a variety of aspects of analysis and geometry on foliated spaces applicable to many contexts, dealing with the topics of locally traceable operators, tangential cohomology, transverse measures, characteristics classes, operator algebras, pseudodifferential operators, and the index theorem. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)

Synopsis:

This book presents a complete proof of Connes' Index Theorem generalized to foliated spaces, including coverage of new developments and applications.

Synopsis:

This book presents a complete proof of Alain Connes Index Theorem generalized to foliated spaces. Connes result is itself an abstraction of the Atiyah-Singer index theorem to the context of foliated manifolds. The book brings together the necessary background from analysis, geometry, and topology. It thus provides a natural introduction to some of the basic ideas and techniques of noncommutative topology. The present edition has improved exposition, an updated bibliography, an index, and additional material covering new developments and applications since the first edition appeared.

About the Author

Calvin C. Moore received his Ph.D. from Harvard in 1960 under George Mackey in topological groups and their representations. His research interests have extended over time to include ergodic theory, operator algebras, and applications of these to number theory, algebra, and geometry. He spent from 1960-61 as Postdoc at the University of Chicago and has been on UC Berkeley Mathematics faculty since 1961. He was co-founder (with S. S. Chern and I. M. Singer) of the Mathematical Sciences Research Institute, and has held various administrative posts within the University of California. He is a Fellow of the American Association for the Advancement of Sciences and the American Academy of Arts and Sciences.Claude L. Schochet received his Ph.D. at the University of Chicago under J. P. May, in algebraic topology. His research interests have extended to include operator algebras, foliated spaces, K-theory and non-commutative topology. He taught at Aarhus University (Denmark), Hebrew University (Jerusalem), Indiana University, and has been at WSU since 1976. Since then, he has spent his year long sabbatical leaves at StonyBrook, UCLA, MSRI, U. Maryland, Technion (Haifa, Israel) and has made shorter visits to many other institutions, including Hautes Etudes Sci., University of Copenhagen, and University of California, Berkeley. He has co-authored an AMS Memoir, edited volumes and published many articles. He is a member of the American Mathematical Society, London Mathematical Society, European Mathematical Society, and Israel Mathematics Union.

Table of Contents

Introduction; 1. Locally traceable operators; 2. Foliated spaces; 3. Tangential cohomology; 4. Transverse measures; 5. Characteristic classes; 6. Operator algebra; 7. Pseudodifferential operators; 8. The index theorem; Appendices.

Product Details

ISBN:
9780521613057
Author:
Moore, Calvin C.
Publisher:
Cambridge University Press
Author:
Schochet, Claude L.
Location:
Cambridge
Subject:
Applied
Subject:
Global analysis (Mathematics)
Subject:
Foliations (Mathematics)
Subject:
Topology - General
Subject:
MATHEMATICS / Topology
Edition Number:
2
Series:
Mathematical Sciences Research Institute Publications
Series Volume:
9
Publication Date:
20051231
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
Y
Pages:
293
Dimensions:
9.26x6.28x.65 in. .97 lbs.

Related Subjects

Science and Mathematics » Mathematics » Geometry » General
Science and Mathematics » Mathematics » Topology

Global Analysis on Foliated Spaces New Trade Paper
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Product details 293 pages Cambridge University Press - English 9780521613057 Reviews:
"Synopsis" by , This book presents a complete proof of Connes' Index Theorem generalized to foliated spaces, including coverage of new developments and applications.
"Synopsis" by , This book presents a complete proof of Alain Connes Index Theorem generalized to foliated spaces. Connes result is itself an abstraction of the Atiyah-Singer index theorem to the context of foliated manifolds. The book brings together the necessary background from analysis, geometry, and topology. It thus provides a natural introduction to some of the basic ideas and techniques of noncommutative topology. The present edition has improved exposition, an updated bibliography, an index, and additional material covering new developments and applications since the first edition appeared.

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