Cargando…
Global analysis on foliated spaces /
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 ge...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Cambridge University Press,
2006.
|
| Edición: | 2nd ed. |
| Colección: | Mathematical Sciences Research Institute publications ;
9. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | 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. |
|---|---|
| Descripción Física: | 1 online resource (xiii, 293 pages) : illustrations |
| Bibliografía: | Includes bibliographical references (pages 267-279) and index. |
| ISBN: | 0511137842 9780511137846 9780511140365 0511140363 1316084973 9781316084977 1280417323 9781280417320 9786610417322 6610417326 0511183259 9780511183256 0511139292 9780511139291 0511311362 9780511311369 0511756364 9780511756368 0511139616 9780511139611 |