Global Analysis on Foliated Spaces

Calvin C. Moore, Claude L. Schochet - Collection Mathematical Sciences Research Institute Publications

296 pages, parution le 23/03/2006 (2^eme édition)

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Résumé

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.

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

Sommaire

Introduction
Locally traceable operators
Foliated spaces
Tangential cohomology
Transverse measures
Characteristic classes
Operator algebra
Pseudodifferential operators
The index theorem
Appendices

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Calvin C. Moore, Claude L. Schochet
Collection	Mathematical Sciences Research Institute Publications
Parution	23/03/2006
Édition	2^eme édition
Nb. de pages	296
Format	15,5 x 23,5
Couverture	Broché
Poids	440g
Intérieur	Noir et Blanc
EAN13	9780521613057
ISBN13	978-0-521-61305-7