Global Analysis on Foliated Spaces
Global Analysis on Foliated Spaces
Claude L. Schochet, Wayne State University, Detroit
Mathematical Sciences Research Institute
£48.99
GBPFoliated 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 and topology. 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 second edition presents a complete proof of this beautiful result, generalized to foliated spaces (not just manifolds). It includes the necessary background from analysis, geometry, and topology. The present edition has improved exposition, an updated bibliography, an index, and additional material covering developments and applications since the first edition came out, including the confirmation of the Gap Labeling Conjecture of Jean Bellissard.
- Background information in all fields necessary to understand the proof of the Index Theorem; fundamental text in non-commutative topology
- Contains new chapter updates, an appendix discussing the Gap Labelling Theorem, an updated bibliography, and completely redone illustrations
- The first edition of the book was widely and positively reviewed
Reviews & endorsements
Praise for the first edition … 'The quest for the proof leads through functional analysis, C^* and von Neumann algebras, topological groupoids, characteristic classes and K-theory along a foliation, and the theory of pseudodifferential operators. It is a long but very rewarding journey and Moore and Schochet have performed a valuable service in putting all this material in one place in an easily readable form … The book contains a wealth of information. It is not for those who wish an overview...However, for those wishing a comprehensive proof … this book is indispensable.' AMS Bulletin
'This book presents a complete proof of this beautiful result, generalized to foliated spaces (not just manifolds). It includes the necessary background from analysis geometry and topology. This second edition has improved exposition, an updated bibliography, an index, and additional material covering developments and applications since the first edition came out.' L'enseignement mathematique
Product details
March 2006Paperback
9780521613057
308 pages
236 × 156 × 18 mm
0.44kg
Available
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.
