Supersymmetry and equivariant de Rham theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
1999
|
| Schriftenreihe: | Mathematics past and present
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverzeichnis Seite 221 - 225 Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | xxiii, 228 Seiten Illustrationen, Diagramme |
| ISBN: | 354064797X 9783540647973 9783642084331 |
Internformat
MARC
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| 100 | 1 | |a Guillemin, Victor |d 1937- |e Verfasser |0 (DE-588)12110172X |4 aut | |
| 245 | 1 | 0 | |a Supersymmetry and equivariant de Rham theory |c Victor W. Guillemin ; Shlomo Sternberg |
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c 1999 | |
| 300 | |a xxiii, 228 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Mathematics past and present | |
| 500 | |a Literaturverzeichnis Seite 221 - 225 | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 7 | |a De Rham, Cohomologie de |2 ram | |
| 650 | 7 | |a Henri Cartan |2 inriac | |
| 650 | 7 | |a Homologie |2 ram | |
| 650 | 7 | |a Supersymétrie |2 ram | |
| 650 | 7 | |a classe caractéristique |2 inriac | |
| 650 | 7 | |a cohomologie De Rham |2 inriac | |
| 650 | 7 | |a géométrie symplectique |2 inriac | |
| 650 | 7 | |a supersymétrie |2 inriac | |
| 650 | 7 | |a théorème De Rham |2 inriac | |
| 650 | 4 | |a Homology theory | |
| 650 | 4 | |a Supersymmetry | |
| 650 | 0 | 7 | |a Äquivariante Kohomologietheorie |0 (DE-588)4288548-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Supersymmetrie |0 (DE-588)4128574-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a DeRham-Theorie |0 (DE-588)4494379-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Äquivariante Kohomologietheorie |0 (DE-588)4288548-6 |D s |
| 689 | 0 | 1 | |a DeRham-Theorie |0 (DE-588)4494379-9 |D s |
| 689 | 0 | 2 | |a Supersymmetrie |0 (DE-588)4128574-8 |D s |
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| 700 | 1 | |a Sternberg, Shlomo |d 1936- |e Verfasser |0 (DE-588)121101762 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-008453925 | ||
Datensatz im Suchindex
| _version_ | 1804127096548622336 |
|---|---|
| adam_text | Contents
Introduction xiii
1 Equivariant Cohomology in Topology 1
1.1 Equivariant Cohomology via Classifying Bundles 1
1.2 Existence of Classifying Spaces 5
1.3 Bibliographical Notes for Chapter 1 6
2 G* Modules 9
2.1 Differential Geometric Identities 9
2.2 The Language of Superalgebra 11
2.3 From Geometry to Algebra 17
2.3.1 Cohomology 19
2.3.2 Acyclicity 20
2.3.3 Chain Homotopies 20
2.3.4 Free Actions and the Condition (C) 23
2.3.5 The Basic Subcomplex 26
2.4 Equivariant Cohomology of G* Algebras 27
2.5 The Equivariant de Rham Theorem 28
2.6 Bibliographical Notes for Chapter 2 31
3 The Weil Algebra 33
3.1 The Koszul Complex 33
3.2 The Weil Algebra 34
3.3 Classifying Maps 37
3.4 W* Modules 39
3.5 Bibliographical Notes for Chapter 3 40
4 The Weil Model and the Cartan Model 41
4.1 The Mathai Quillen Isomorphism 41
4.2 The Cartan Model 44
4.3 Equivariant Cohomology of W* Modules 46
4.4 H ({A g £)bas) does not depend on E 48
4.5 The Characteristic Homomorphism 48
4.6 Commuting Actions 49
x Contents
4.7 The Equivariant Cohomology of
Homogeneous Spaces 50
4.8 Exact Sequences 51
4.9 Bibliographical Notes for Chapter 4 51
5 Cartan s Formula 53
5.1 The Cartan Model for W* Modules 54
5.2 Cartan s Formula 57
5.3 Bibliographical Notes for Chapter 5 59
6 Spectral Sequences 61
6.1 Spectral Sequences of Double Complexes 61
6.2 The First Term 66
6.3 The Long Exact Sequence 67
6.4 Useful Facts for Doing Computations 68
6.4.1 Functorial Behavior 68
6.4.2 Gaps 68
6.4.3 Switching Rows and Columns 69
6.5 The Cartan Model as a Double Complex 69
6.6 HG(A) as an 5(5*)G Module 71
6.7 Morphisms of G* Modules 71
6.8 Restricting the Group 72
6.9 Bibliographical Notes for Chapter 6 75
7 Fermionic Integration 77
7.1 Definition and Elementary Properties 77
7.1.1 Integration by Parts 78
7.1.2 Change of Variables 78
7.1.3 Gaussian Integrals 79
7.1.4 Iterated Integrals 80
7.1.5 The Fourier Transform 81
7.2 The Mathai Quillen Construction 85
7.3 The Fourier Transform of the Koszul Complex 88
7.4 Bibliographical Notes for Chapter 7 92
8 Characteristic Classes 95
8.1 Vector Bundles • ¦ • ¦ • 95
8.2 The Invariants 96
8.2.1 G=U(n) 96
8.2.2 G = O(n) 97
8.2.3 G = SO(2n) 97
8.3 Relations Between the Invariants 98
8.3.1 Restriction from U(n) to O{n) 99
8.3.2 Restriction from SO(2n) to U(n) 100
8.3.3 Restriction from U{n) to U{k) x U{£) 100
Contents xi
8.4 Symplectic Vector Bundles 101
8.4.1 Consistent Complex Structures 101
8.4.2 Characteristic Classes of Symplectic Vector Bundles . 103
8.5 Equivariant Characteristic Classes 104
8.5.1 Equivariant Chern classes 104
8.5.2 Equivariant Characteristic Classes of a
Vector Bundle Over a Point 104
8.5.3 Equivariant Characteristic Classes as Fixed Point DatalO5
8.6 The Splitting Principle in Topology 106
8.7 Bibliographical Notes for Chapter 8 108
9 Equivariant Symplectic Forms 111
9.1 Equivariantly Closed Two Forms Ill
9.2 The Case M = G 112
9.3 Equivariantly Closed Two Forms on
Homogeneous Spaces 114
9.4 The Compact Case 115
9.5 Minimal Coupling 116
9.6 Symplectic Reduction 117
9.7 The Duistermaat Heckman Theorem 120
9.8 The Cohomology Ring of Reduced Spaces 121
9.8.1 Flag Manifolds 124
9.8.2 Delzant Spaces 126
9.8.3 Reduction: The Linear Case 130
9.9 Equivariant Duistermaat Heckman 132
9.10 Group Valued Moment Maps 134
9.10.1 The Canonical Equivariant Closed Three Form on G 135
9.10.2 The Exponential Map 138
9.10.3 G Valued Moment Maps on
Hamiltonian G Manifolds 141
9.10.4 Conjugacy Classes 143
9.11 Bibliographical Notes for Chapter 9 145
10 The Thorn Class and Localization 149
10.1 Fiber Integration of Equivariant Forms 150
10.2 The Equivariant Normal Bundle 154
10.3 Modifying v 156
10.4 Verifying that r is a Thorn Form 156
10.5 The Thorn Class and the Euler Class 158
10.6 The Fiber Integral on Cohomology 159
10.7 Push Forward in General 159
10.8 Localization 160
10.9 The Localization for Torus Actions 163
10.10 Bibliographical Notes for Chapter 10 168
xii Contents
11 The Abstract Localization Theorem 173
11.1 Relative Equivariant de Rham Theory 173
11.2 Mayer Vietoris 175
11.3 S(#*) Modules 175
11.4 The Abstract Localization Theorem 176
11.5 The Chang Skjelbred Theorem 179
11.6 Some Consequences of Equivariant
Formality 180
11.7 Two Dimensional G Manifolds 180
11.8 A Theorem of Goresky Kottwitz MacPherson 183
11.9 Bibliographical Notes for Chapter 11 185
Appendix 189
Notions d algebre differentielle; application aux groupes de Lie et
aux varietes ou opere un groupe de Lie
Henri Cartan 191
La transgression dans un groupe de Lie et dans un espace fibre
principal
Henri Cartan 205
Bibliography 221
Index . 227
|
| any_adam_object | 1 |
| author | Guillemin, Victor 1937- Sternberg, Shlomo 1936- |
| author_GND | (DE-588)12110172X (DE-588)121101762 |
| author_facet | Guillemin, Victor 1937- Sternberg, Shlomo 1936- |
| author_role | aut aut |
| author_sort | Guillemin, Victor 1937- |
| author_variant | v g vg s s ss |
| building | Verbundindex |
| bvnumber | BV012457784 |
| classification_rvk | SK 260 SK 320 SK 350 UO 1560 |
| classification_tum | MAT 143f |
| ctrlnum | (OCoLC)468693033 (DE-599)BVBBV012457784 |
| dewey-full | 516.362 514.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry 514 - Topology |
| dewey-raw | 516.362 514.23 |
| dewey-search | 516.362 514.23 |
| dewey-sort | 3516.362 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV012457784 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:27:55Z |
| institution | BVB |
| isbn | 354064797X 9783540647973 9783642084331 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008453925 |
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| physical | xxiii, 228 Seiten Illustrationen, Diagramme |
| publishDate | 1999 |
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| spelling | Guillemin, Victor 1937- Verfasser (DE-588)12110172X aut Supersymmetry and equivariant de Rham theory Victor W. Guillemin ; Shlomo Sternberg Berlin ; Heidelberg Springer 1999 xxiii, 228 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematics past and present Literaturverzeichnis Seite 221 - 225 Hier auch später erschienene, unveränderte Nachdrucke De Rham, Cohomologie de ram Henri Cartan inriac Homologie ram Supersymétrie ram classe caractéristique inriac cohomologie De Rham inriac géométrie symplectique inriac supersymétrie inriac théorème De Rham inriac Homology theory Supersymmetry Äquivariante Kohomologietheorie (DE-588)4288548-6 gnd rswk-swf Supersymmetrie (DE-588)4128574-8 gnd rswk-swf DeRham-Theorie (DE-588)4494379-9 gnd rswk-swf Äquivariante Kohomologietheorie (DE-588)4288548-6 s DeRham-Theorie (DE-588)4494379-9 s Supersymmetrie (DE-588)4128574-8 s DE-604 Sternberg, Shlomo 1936- Verfasser (DE-588)121101762 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008453925&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Guillemin, Victor 1937- Sternberg, Shlomo 1936- Supersymmetry and equivariant de Rham theory De Rham, Cohomologie de ram Henri Cartan inriac Homologie ram Supersymétrie ram classe caractéristique inriac cohomologie De Rham inriac géométrie symplectique inriac supersymétrie inriac théorème De Rham inriac Homology theory Supersymmetry Äquivariante Kohomologietheorie (DE-588)4288548-6 gnd Supersymmetrie (DE-588)4128574-8 gnd DeRham-Theorie (DE-588)4494379-9 gnd |
| subject_GND | (DE-588)4288548-6 (DE-588)4128574-8 (DE-588)4494379-9 |
| title | Supersymmetry and equivariant de Rham theory |
| title_auth | Supersymmetry and equivariant de Rham theory |
| title_exact_search | Supersymmetry and equivariant de Rham theory |
| title_full | Supersymmetry and equivariant de Rham theory Victor W. Guillemin ; Shlomo Sternberg |
| title_fullStr | Supersymmetry and equivariant de Rham theory Victor W. Guillemin ; Shlomo Sternberg |
| title_full_unstemmed | Supersymmetry and equivariant de Rham theory Victor W. Guillemin ; Shlomo Sternberg |
| title_short | Supersymmetry and equivariant de Rham theory |
| title_sort | supersymmetry and equivariant de rham theory |
| topic | De Rham, Cohomologie de ram Henri Cartan inriac Homologie ram Supersymétrie ram classe caractéristique inriac cohomologie De Rham inriac géométrie symplectique inriac supersymétrie inriac théorème De Rham inriac Homology theory Supersymmetry Äquivariante Kohomologietheorie (DE-588)4288548-6 gnd Supersymmetrie (DE-588)4128574-8 gnd DeRham-Theorie (DE-588)4494379-9 gnd |
| topic_facet | De Rham, Cohomologie de Henri Cartan Homologie Supersymétrie classe caractéristique cohomologie De Rham géométrie symplectique supersymétrie théorème De Rham Homology theory Supersymmetry Äquivariante Kohomologietheorie Supersymmetrie DeRham-Theorie |
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