Global Analysis on Foliated Spaces (Paperback)

Calvin C. Moore

ISBN 10: 0521613051 / ISBN 13: 9780521613057

Edité par Cambridge University Press, Cambridge, 2006

A propos de cet article

Paperback. 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. 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). Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

N° de réf. du vendeur 9780521613057

Détails bibliographiques

• Titre: Global Analysis on Foliated Spaces (Paperback)
• Éditeur: Cambridge University Press, Cambridge
• Date de parution: 2006
• Langue: anglais
• ISBN à 10 chiffres: 0521613051
• ISBN à 13 chiffres: 9780521613057
• Reliure: Paperback
• Édition: 2ème Édition
• État de l'article: new

A propos de ce titre

Synopsis

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

À propos des auteurs

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.