The heat kernel Lefschetz fixed point formula for the spin-c Dirac operator:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
1996
|
| Series: | Progress in nonlinear differential equations and their applications
18 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 247 S. |
| ISBN: | 0817638652 3764338652 |
Staff View
MARC
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| 100 | 1 | |a Duistermaat, Johannes J. |d 1942-2010 |e Verfasser |0 (DE-588)121717070 |4 aut | |
| 245 | 1 | 0 | |a The heat kernel Lefschetz fixed point formula for the spin-c Dirac operator |c J. J. Duistermaat |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1996 | |
| 300 | |a VII, 247 S. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Introduction 1
1.1 The Holomorphic Lefschetz Fixed Point Formula 1
1.2 The Heat Kernel 2
1.3 The Results 3
2 The Dolbeault Dirac Operator 7
2.1 The Dolbeault Complex 7
2.2 The Dolbeault Dirac Operator 12
3 Clifford Modules 19
3.1 The Non Kahler Case 19
3.2 The Clifford Algebra 22
3.3 The Supertrace 27
3.4 The Clifford Bundle 29
4 The Spin Group and the Spin c Group 35
4.1 The Spin Group 35
4.2 The Spin c Group 37
4.3 Proof of a Formula for the Supertrace 39
5 The Spin c Dirac Operator 41
5.1 The Spin c Frame Bundle and Connections 41
5.2 Definition of the Spin c Dirac Operator 47
v
vi Contents
6 Its Square 53
6.1 Its Square 53
6.2 Dirac Operators on Spinor Bundles 61
6.3 The Kahler Case 63
7 The Heat Kernel Method 69
7.1 Traces 69
7.2 The Heat Diffusion Operator 72
8 The Heat Kernel Expansion 77
8.1 The Laplace Operator 77
8.2 Construction of the Heat Kernel 79
8.3 The Square of the Geodesic Distance 81
8.4 The Expansion 92
9 The Heat Kernel on a Principal Bundle 99
9.1 Introduction 99
9.2 The Laplace Operator on P 100
9.3 The Zero Order Term 105
9.4 The Heat Kernel 108
9.5 The Expansion 110
10 The Automorphism 117
10.1 Assumptions 117
10.2 An Estimate for Geodesies in P 121
10.3 The Expansion 125
11 The Hirzebruch Riemann Roch Integrand 131
11.1 Introduction 131
11.2 Computations in the Exterior Algebra 133
11.3 The Short Time Limit of the Supertrace 143
Contents vii
12 The Local Lefschetz Fixed Point Formula 147
12.1 The Element g0 of the Structure Group 147
12.2 The Short Time Limit 151
12.3 The Kahler Case 155
13 Characteristic Classes 157
13.1 Weil s Homomorphism 157
13.2 The Chern Matrix and the Riemann Roch Formula .... 159
13.3 The Lefschetz Formula 164
13.4 A Simple Example 169
14 The Orbifold Version 171
14.1 Orbifolds 171
14.2 The Virtual Character 176
14.3 The Heat Kernel Method 177
14.4 The Fixed Point Orbifolds 179
14.5 The Normal Eigenbundles 181
14.6 The Lefschetz Formula 183
15 Application to Symplectic Geometry 187
15.1 Symplectic Manifolds 188
15.2 Hamiltonian Group Actions and Reduction 192
15.3 The Complex Line Bundle 201
15.4 Lifting the Action 205
15.5 The Spin c Dirac Operator 213
16 Appendix: Equivariant Forms 221
16.1 Equivariant Cohomology 221
16.2 Existence of a Connection Form 225
16.3 Henri Cartan s Theorem 227
16.4 Proof of Weil s Theorem 234
16.5 General Actions 234
|
| any_adam_object | 1 |
| author | Duistermaat, Johannes J. 1942-2010 |
| author_GND | (DE-588)121717070 |
| author_facet | Duistermaat, Johannes J. 1942-2010 |
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| id | DE-604.BV010588225 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:55:32Z |
| institution | BVB |
| isbn | 0817638652 3764338652 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007060301 |
| oclc_num | 612842120 |
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| owner_facet | DE-91G DE-BY-TUM DE-12 DE-355 DE-BY-UBR DE-384 DE-703 DE-634 DE-19 DE-BY-UBM DE-11 DE-188 |
| physical | VII, 247 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in nonlinear differential equations and their applications |
| series2 | Progress in nonlinear differential equations and their applications |
| spelling | Duistermaat, Johannes J. 1942-2010 Verfasser (DE-588)121717070 aut The heat kernel Lefschetz fixed point formula for the spin-c Dirac operator J. J. Duistermaat Boston [u.a.] Birkhäuser 1996 VII, 247 S. txt rdacontent n rdamedia nc rdacarrier Progress in nonlinear differential equations and their applications 18 Dirac-Operator (DE-588)4150118-4 gnd rswk-swf Kern Mathematik (DE-588)4163599-1 gnd rswk-swf Dirac-Operator (DE-588)4150118-4 s Kern Mathematik (DE-588)4163599-1 s DE-604 Progress in nonlinear differential equations and their applications 18 (DE-604)BV007934389 18 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007060301&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Duistermaat, Johannes J. 1942-2010 The heat kernel Lefschetz fixed point formula for the spin-c Dirac operator Progress in nonlinear differential equations and their applications Dirac-Operator (DE-588)4150118-4 gnd Kern Mathematik (DE-588)4163599-1 gnd |
| subject_GND | (DE-588)4150118-4 (DE-588)4163599-1 |
| title | The heat kernel Lefschetz fixed point formula for the spin-c Dirac operator |
| title_auth | The heat kernel Lefschetz fixed point formula for the spin-c Dirac operator |
| title_exact_search | The heat kernel Lefschetz fixed point formula for the spin-c Dirac operator |
| title_full | The heat kernel Lefschetz fixed point formula for the spin-c Dirac operator J. J. Duistermaat |
| title_fullStr | The heat kernel Lefschetz fixed point formula for the spin-c Dirac operator J. J. Duistermaat |
| title_full_unstemmed | The heat kernel Lefschetz fixed point formula for the spin-c Dirac operator J. J. Duistermaat |
| title_short | The heat kernel Lefschetz fixed point formula for the spin-c Dirac operator |
| title_sort | the heat kernel lefschetz fixed point formula for the spin c dirac operator |
| topic | Dirac-Operator (DE-588)4150118-4 gnd Kern Mathematik (DE-588)4163599-1 gnd |
| topic_facet | Dirac-Operator Kern Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007060301&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV007934389 |
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