Global Analysis on Foliated Spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1988
|
| Schriftenreihe: | Mathematical Sciences Research Institute Publications
9 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Global analysis has as its primary focus the interplay between the local analysis and the global geometry and topology of a manifold. This is seen classicallv in the Gauss-Bonnet theorem and its generalizations. which culminate in the Ativah-Singer Index Theorem [ASI] which places constraints on the solutions of elliptic systems of partial differential equations in terms of the Fredholm index of the associated elliptic operator and characteristic differential forms which are related to global topologie al properties of the manifold. The Ativah-Singer Index Theorem has been generalized in several directions. notably by Atiyah-Singer to an index theorem for families [AS4]. The typical setting here is given by a family of elliptic operators (Pb) on the total space of a fibre bundle P = F_M_B. where is defined the Hilbert space on Pb 2 L 1p -llbl.dvollFll. In this case there is an abstract index class indlPI E ROIBI. Once the problem is properly formulated it turns out that no further deep analvtic information is needed in order to identify the class. These theorems and their equivariant counterparts have been enormously useful in topology. geometry. physics. and in representation theory |
| Beschreibung: | 1 Online-Ressource (VII, 337p. 16 illus) |
| ISBN: | 9781461395928 9781461395942 |
| ISSN: | 0940-4740 |
| DOI: | 10.1007/978-1-4613-9592-8 |
Internformat
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| 500 | |a Global analysis has as its primary focus the interplay between the local analysis and the global geometry and topology of a manifold. This is seen classicallv in the Gauss-Bonnet theorem and its generalizations. which culminate in the Ativah-Singer Index Theorem [ASI] which places constraints on the solutions of elliptic systems of partial differential equations in terms of the Fredholm index of the associated elliptic operator and characteristic differential forms which are related to global topologie al properties of the manifold. The Ativah-Singer Index Theorem has been generalized in several directions. notably by Atiyah-Singer to an index theorem for families [AS4]. The typical setting here is given by a family of elliptic operators (Pb) on the total space of a fibre bundle P = F_M_B. where is defined the Hilbert space on Pb 2 L 1p -llbl.dvollFll. In this case there is an abstract index class indlPI E ROIBI. Once the problem is properly formulated it turns out that no further deep analvtic information is needed in order to identify the class. These theorems and their equivariant counterparts have been enormously useful in topology. geometry. physics. and in representation theory | ||
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Datensatz im Suchindex
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| dewey-full | 514.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.2 |
| dewey-search | 514.2 |
| dewey-sort | 3514.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4613-9592-8 |
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| id | DE-604.BV042420809 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461395928 9781461395942 |
| issn | 0940-4740 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856226 |
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| physical | 1 Online-Ressource (VII, 337p. 16 illus) |
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| publishDate | 1988 |
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| spelling | Moore, Calvin C. 1936- Verfasser (DE-588)1077542534 aut Global Analysis on Foliated Spaces by Calvin C. Moore, Claude Schochet New York, NY Springer New York 1988 1 Online-Ressource (VII, 337p. 16 illus) txt rdacontent c rdamedia cr rdacarrier Mathematical Sciences Research Institute Publications 9 0940-4740 Global analysis has as its primary focus the interplay between the local analysis and the global geometry and topology of a manifold. This is seen classicallv in the Gauss-Bonnet theorem and its generalizations. which culminate in the Ativah-Singer Index Theorem [ASI] which places constraints on the solutions of elliptic systems of partial differential equations in terms of the Fredholm index of the associated elliptic operator and characteristic differential forms which are related to global topologie al properties of the manifold. The Ativah-Singer Index Theorem has been generalized in several directions. notably by Atiyah-Singer to an index theorem for families [AS4]. The typical setting here is given by a family of elliptic operators (Pb) on the total space of a fibre bundle P = F_M_B. where is defined the Hilbert space on Pb 2 L 1p -llbl.dvollFll. In this case there is an abstract index class indlPI E ROIBI. Once the problem is properly formulated it turns out that no further deep analvtic information is needed in order to identify the class. These theorems and their equivariant counterparts have been enormously useful in topology. geometry. physics. and in representation theory Mathematics Algebraic topology Algebraic Topology Theoretical, Mathematical and Computational Physics Mathematik Globale Analysis (DE-588)4021285-3 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Faltungsgleichung (DE-588)4368138-4 gnd rswk-swf Raum Mathematik (DE-588)4124030-3 gnd rswk-swf Blätterung (DE-588)4007006-2 gnd rswk-swf Blätterung (DE-588)4007006-2 s Globale Analysis (DE-588)4021285-3 s 1\p DE-604 Raum Mathematik (DE-588)4124030-3 s 2\p DE-604 Analysis (DE-588)4001865-9 s 3\p DE-604 Faltungsgleichung (DE-588)4368138-4 s 4\p DE-604 Schochet, Claude 1944- Sonstige (DE-588)172361974 oth https://doi.org/10.1007/978-1-4613-9592-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Moore, Calvin C. 1936- Global Analysis on Foliated Spaces Mathematics Algebraic topology Algebraic Topology Theoretical, Mathematical and Computational Physics Mathematik Globale Analysis (DE-588)4021285-3 gnd Analysis (DE-588)4001865-9 gnd Faltungsgleichung (DE-588)4368138-4 gnd Raum Mathematik (DE-588)4124030-3 gnd Blätterung (DE-588)4007006-2 gnd |
| subject_GND | (DE-588)4021285-3 (DE-588)4001865-9 (DE-588)4368138-4 (DE-588)4124030-3 (DE-588)4007006-2 |
| 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 by Calvin C. Moore, Claude Schochet |
| title_fullStr | Global Analysis on Foliated Spaces by Calvin C. Moore, Claude Schochet |
| title_full_unstemmed | Global Analysis on Foliated Spaces by Calvin C. Moore, Claude Schochet |
| title_short | Global Analysis on Foliated Spaces |
| title_sort | global analysis on foliated spaces |
| topic | Mathematics Algebraic topology Algebraic Topology Theoretical, Mathematical and Computational Physics Mathematik Globale Analysis (DE-588)4021285-3 gnd Analysis (DE-588)4001865-9 gnd Faltungsgleichung (DE-588)4368138-4 gnd Raum Mathematik (DE-588)4124030-3 gnd Blätterung (DE-588)4007006-2 gnd |
| topic_facet | Mathematics Algebraic topology Algebraic Topology Theoretical, Mathematical and Computational Physics Mathematik Globale Analysis Analysis Faltungsgleichung Raum Mathematik Blätterung |
| url | https://doi.org/10.1007/978-1-4613-9592-8 |
| work_keys_str_mv | AT moorecalvinc globalanalysisonfoliatedspaces AT schochetclaude globalanalysisonfoliatedspaces |