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 g...
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2006
|
| Ausgabe: | Second edition. |
| Schriftenreihe: | Mathematical Sciences Research Institute publications
9 |
| Links: | https://doi.org/10.1017/CBO9780511756368 |
| Zusammenfassung: | 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. |
| Umfang: | 1 Online-Ressource (xiii, 293 Seiten) |
| ISBN: | 9780511756368 |
Internformat
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| 520 | |a 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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| spelling | Moore, C. C. 1936- Global analysis on foliated spaces Calvin C. Moore, Claude L. Schochet Second edition. Cambridge Cambridge University Press 2006 1 Online-Ressource (xiii, 293 Seiten) txt c cr Mathematical Sciences Research Institute publications 9 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. Schochet, Claude 1944- Erscheint auch als Druck-Ausgabe 9780521613057 |
| spellingShingle | Moore, C. C. 1936- Global analysis on foliated spaces |
| title | Global analysis on foliated spaces |
| title_auth | Global analysis on foliated spaces |
| title_exact_search | Global analysis on foliated spaces |
| title_full | Global analysis on foliated spaces Calvin C. Moore, Claude L. Schochet |
| title_fullStr | Global analysis on foliated spaces Calvin C. Moore, Claude L. Schochet |
| title_full_unstemmed | Global analysis on foliated spaces Calvin C. Moore, Claude L. Schochet |
| title_short | Global analysis on foliated spaces |
| title_sort | global analysis on foliated spaces |
| work_keys_str_mv | AT moorecc globalanalysisonfoliatedspaces AT schochetclaude globalanalysisonfoliatedspaces |