Calvin C. Moore

Global Analysis on Foliated Spaces (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 19. Dezember 2005
• Englisch
• ISBN-13: 9780511137846
• Artikelnr.: 38206074

Autorenporträt

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.

Inhaltsangabe

I. Locally Traceable Operators.- II. Foliated Spaces.- III. Tangential Cohomology.- IV. Transverse Measures.- V. Characteristic Classes.- VI. Operator Algebras.- VII. Pseudodifferential Operators.- VIII. The Index Theorem.- Appendices.- C: Positive Scalar Curvature Along the Leaves.- References.

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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.