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...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York :
Cambridge University Press,
2006.
|
| Ausgabe: | 2nd ed. |
| Schriftenreihe: | Mathematical Sciences Research Institute publications ;
9. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| 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. |
| Beschreibung: | 1 online resource (xiii, 293 pages) : illustrations |
| Bibliographie: | 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 |
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| author | Moore, C. C. (Calvin C.), 1936- |
| author2 | Schochet, Claude, 1944- |
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| contents | Locally traceable operators -- Foliated spaces -- Tangential cohomology -- Transverse measures -- Characteristic classes -- Operator algebras -- Pseudodifferential operators -- The index theorem. |
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| series | Mathematical Sciences Research Institute publications ; |
| series2 | Mathematical Sciences Research Institute publications ; |
| spelling | Moore, C. C. (Calvin C.), 1936- https://id.oclc.org/worldcat/entity/E39PBJjdkmXrjhVcHPBcTBk7HC http://id.loc.gov/authorities/names/n86109624 Global analysis on foliated spaces / Calvin C. Moore, Claude L. Schochet. 2nd ed. New York : Cambridge University Press, 2006. 1 online resource (xiii, 293 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Mathematical Sciences Research Institute publications ; 9 Includes bibliographical references (pages 267-279) and index. Print version record. Locally traceable operators -- Foliated spaces -- Tangential cohomology -- Transverse measures -- Characteristic classes -- Operator algebras -- Pseudodifferential operators -- The index theorem. 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. English. Global analysis (Mathematics) http://id.loc.gov/authorities/subjects/sh85055284 Foliations (Mathematics) http://id.loc.gov/authorities/subjects/sh85049646 Analyse globale (Mathématiques) Feuilletages (Mathématiques) MATHEMATICS Topology. bisacsh Foliations (Mathematics) fast Global analysis (Mathematics) fast Electronic books. Schochet, Claude, 1944- https://id.oclc.org/worldcat/entity/E39PCjJG9f87CFqFQHX8wwH9jC http://id.loc.gov/authorities/names/n82038796 Print version: Moore, C.C. (Calvin C.), 1936- Global analysis on foliated spaces. 2nd ed. New York : Cambridge University Press, 2006 0521613051 (DLC) 2005054277 (OCoLC)61652875 Mathematical Sciences Research Institute publications ; 9. http://id.loc.gov/authorities/names/n84714376 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=148121 Volltext |
| spellingShingle | Moore, C. C. (Calvin C.), 1936- Global analysis on foliated spaces / Mathematical Sciences Research Institute publications ; Locally traceable operators -- Foliated spaces -- Tangential cohomology -- Transverse measures -- Characteristic classes -- Operator algebras -- Pseudodifferential operators -- The index theorem. Global analysis (Mathematics) http://id.loc.gov/authorities/subjects/sh85055284 Foliations (Mathematics) http://id.loc.gov/authorities/subjects/sh85049646 Analyse globale (Mathématiques) Feuilletages (Mathématiques) MATHEMATICS Topology. bisacsh Foliations (Mathematics) fast Global analysis (Mathematics) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85055284 http://id.loc.gov/authorities/subjects/sh85049646 |
| 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 |
| topic | Global analysis (Mathematics) http://id.loc.gov/authorities/subjects/sh85055284 Foliations (Mathematics) http://id.loc.gov/authorities/subjects/sh85049646 Analyse globale (Mathématiques) Feuilletages (Mathématiques) MATHEMATICS Topology. bisacsh Foliations (Mathematics) fast Global analysis (Mathematics) fast |
| topic_facet | Global analysis (Mathematics) Foliations (Mathematics) Analyse globale (Mathématiques) Feuilletages (Mathématiques) MATHEMATICS Topology. Electronic books. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=148121 |
| work_keys_str_mv | AT moorecc globalanalysisonfoliatedspaces AT schochetclaude globalanalysisonfoliatedspaces |