Spin Geometry:
This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas requ...
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| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[2016]
|
| Schriftenreihe: | Princeton mathematical series
38 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas require various general forms of the Atiyah-Singer Index Theorem, the theorems and their proofs, together with all prerequisite material, are examined here in detail. The exposition is richly embroidered with examples and applications to a wide spectrum of problems in differential geometry, topology, and mathematical physics. The authors consistently use Clifford algebras and their representations in this exposition. Clifford multiplication and Dirac operator identities are even used in place of the standard tensor calculus. This unique approach unifies all the standard elliptic operators in geometry and brings fresh insights into curvature calculations. The fundamental relationships of Clifford modules to such topics as the theory of Lie groups, K-theory, KR-theory, and Bott Periodicity also receive careful consideration. A special feature of this book is the development of the theory of Cl-linear elliptic operators and the associated index theorem, which connects certain subtle spin-corbordism invariants to classical questions in geometry and has led to some of the most profound relations known between the curvature and topology of manifolds |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed Oct. 27, 2016) |
| Beschreibung: | 1 online resource |
| ISBN: | 9781400883912 |
| DOI: | 10.1515/9781400883912 |
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| 520 | |a This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas require various general forms of the Atiyah-Singer Index Theorem, the theorems and their proofs, together with all prerequisite material, are examined here in detail. The exposition is richly embroidered with examples and applications to a wide spectrum of problems in differential geometry, topology, and mathematical physics. The authors consistently use Clifford algebras and their representations in this exposition. Clifford multiplication and Dirac operator identities are even used in place of the standard tensor calculus. This unique approach unifies all the standard elliptic operators in geometry and brings fresh insights into curvature calculations. The fundamental relationships of Clifford modules to such topics as the theory of Lie groups, K-theory, KR-theory, and Bott Periodicity also receive careful consideration. A special feature of this book is the development of the theory of Cl-linear elliptic operators and the associated index theorem, which connects certain subtle spin-corbordism invariants to classical questions in geometry and has led to some of the most profound relations known between the curvature and topology of manifolds | ||
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Datensatz im Suchindex
| _version_ | 1804176944307109888 |
|---|---|
| any_adam_object | |
| author | Lawson, H. Blaine 1942- Michelsohn, Marie-Louise 1941- |
| author_GND | (DE-588)122158814 (DE-588)1048229130 |
| author_facet | Lawson, H. Blaine 1942- Michelsohn, Marie-Louise 1941- |
| author_role | aut aut |
| author_sort | Lawson, H. Blaine 1942- |
| author_variant | h b l hb hbl m l m mlm |
| building | Verbundindex |
| bvnumber | BV043979316 |
| collection | ZDB-23-DGG ZDB-23-PMS |
| ctrlnum | (ZDB-23-DGG)9781400883912 (OCoLC)1165506784 (DE-599)BVBBV043979316 |
| dewey-full | 539.7/25 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 539 - Modern physics |
| dewey-raw | 539.7/25 |
| dewey-search | 539.7/25 |
| dewey-sort | 3539.7 225 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| doi_str_mv | 10.1515/9781400883912 |
| format | Electronic eBook |
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| id | DE-604.BV043979316 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:40:13Z |
| institution | BVB |
| isbn | 9781400883912 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029387753 |
| oclc_num | 1165506784 |
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| physical | 1 online resource |
| psigel | ZDB-23-DGG ZDB-23-PMS |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Princeton mathematical series |
| series2 | Princeton mathematical series |
| spelling | Lawson, H. Blaine 1942- (DE-588)122158814 aut Spin Geometry H. Blaine Lawson, Marie-Louise Michelsohn Princeton, NJ Princeton University Press [2016] © 1990 1 online resource txt rdacontent c rdamedia cr rdacarrier Princeton mathematical series 38 Description based on online resource; title from PDF title page (publisher's Web site, viewed Oct. 27, 2016) This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas require various general forms of the Atiyah-Singer Index Theorem, the theorems and their proofs, together with all prerequisite material, are examined here in detail. The exposition is richly embroidered with examples and applications to a wide spectrum of problems in differential geometry, topology, and mathematical physics. The authors consistently use Clifford algebras and their representations in this exposition. Clifford multiplication and Dirac operator identities are even used in place of the standard tensor calculus. This unique approach unifies all the standard elliptic operators in geometry and brings fresh insights into curvature calculations. The fundamental relationships of Clifford modules to such topics as the theory of Lie groups, K-theory, KR-theory, and Bott Periodicity also receive careful consideration. A special feature of this book is the development of the theory of Cl-linear elliptic operators and the associated index theorem, which connects certain subtle spin-corbordism invariants to classical questions in geometry and has led to some of the most profound relations known between the curvature and topology of manifolds In English Clifford algebras Spin geometry Spinor (DE-588)4182327-8 gnd rswk-swf Indextheorie (DE-588)4161489-6 gnd rswk-swf Spinoranalysis (DE-588)4182329-1 gnd rswk-swf Clifford-Algebra (DE-588)4199958-7 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Kernspin (DE-588)4163636-3 gnd rswk-swf Kernspin (DE-588)4163636-3 s Clifford-Algebra (DE-588)4199958-7 s DE-604 Mathematische Methode (DE-588)4155620-3 s 1\p DE-604 Indextheorie (DE-588)4161489-6 s Spinor (DE-588)4182327-8 s 2\p DE-604 Spinoranalysis (DE-588)4182329-1 s 3\p DE-604 Michelsohn, Marie-Louise 1941- (DE-588)1048229130 aut Princeton mathematical series 38 (DE-604)BV045898993 38 https://doi.org/10.1515/9781400883912?locatt=mode:legacy Verlag URL des Erstveröffentlichers 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 |
| spellingShingle | Lawson, H. Blaine 1942- Michelsohn, Marie-Louise 1941- Spin Geometry Princeton mathematical series Clifford algebras Spin geometry Spinor (DE-588)4182327-8 gnd Indextheorie (DE-588)4161489-6 gnd Spinoranalysis (DE-588)4182329-1 gnd Clifford-Algebra (DE-588)4199958-7 gnd Mathematische Methode (DE-588)4155620-3 gnd Kernspin (DE-588)4163636-3 gnd |
| subject_GND | (DE-588)4182327-8 (DE-588)4161489-6 (DE-588)4182329-1 (DE-588)4199958-7 (DE-588)4155620-3 (DE-588)4163636-3 |
| title | Spin Geometry |
| title_auth | Spin Geometry |
| title_exact_search | Spin Geometry |
| title_full | Spin Geometry H. Blaine Lawson, Marie-Louise Michelsohn |
| title_fullStr | Spin Geometry H. Blaine Lawson, Marie-Louise Michelsohn |
| title_full_unstemmed | Spin Geometry H. Blaine Lawson, Marie-Louise Michelsohn |
| title_short | Spin Geometry |
| title_sort | spin geometry |
| topic | Clifford algebras Spin geometry Spinor (DE-588)4182327-8 gnd Indextheorie (DE-588)4161489-6 gnd Spinoranalysis (DE-588)4182329-1 gnd Clifford-Algebra (DE-588)4199958-7 gnd Mathematische Methode (DE-588)4155620-3 gnd Kernspin (DE-588)4163636-3 gnd |
| topic_facet | Clifford algebras Spin geometry Spinor Indextheorie Spinoranalysis Clifford-Algebra Mathematische Methode Kernspin |
| url | https://doi.org/10.1515/9781400883912?locatt=mode:legacy |
| volume_link | (DE-604)BV045898993 |
| work_keys_str_mv | AT lawsonhblaine spingeometry AT michelsohnmarielouise spingeometry |