Book Details
Format
Paperback / Softback
ISBN-10
0521613051
ISBN-13
9780521613057
Edition
2 Revised edition
Publisher
Cambridge University Press
Imprint
Cambridge University Press
Country of Manufacture
US
Country of Publication
GB
Publication Date
Dec 19th, 2005
Print length
308 Pages
Weight
440 grams
Dimensions
23.60 x 15.60 x 1.80 cms
Product Classification:
Analytic geometry
Ksh 9,200.00
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Presents a complete proof of Connes' Index Theorem generalized to foliated spaces, alongside the necessary background from analysis, geometry, and topology. It thus provides a natural introduction to the basic ideas of noncommutative topology. This edition has improved exposition, an updated bibliography, an index, and covers new developments and applications.
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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