Global Analysis on Foliated Spaces (Mathematical Sciences Research Institute Publications) （2ND）

Moore, Calvin C./ Schochet, Claude L.

Cambridge University Press（2005/12発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 308 p.
• 言語 ENG
• 商品コード 9780521613057
• DDC分類 516.3

Full Description

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.

Contents

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.