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Global Analysis on Foliated Spaces: Mathematical Sciences Research Institute Publications, cartea 9

Autor Calvin C. Moore, Claude L. Schochet
en Limba Engleză Paperback – 18 dec 2005
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 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.
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Specificații

ISBN-13: 9780521613057
ISBN-10: 0521613051
Pagini: 308
Dimensiuni: 156 x 236 x 18 mm
Greutate: 0.44 kg
Ediția:2Revizuită
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Mathematical Sciences Research Institute Publications

Locul publicării:New York, United States

Cuprins

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.

Recenzii

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

Notă biografică


Descriere

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