Index- and spectral theory for manifolds with generalized fibred cusps:
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Bonn
[Math.-Naturwiss. Fak. der Univ.]
2001
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| Series: | Bonner mathematische Schriften
344 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 124 S. graph. Darst. |
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Record in the Search Index
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| adam_text | Titel: Index and spectral theory for manifolds with generalized fibred cusps
Autor: Vaillant, Boris
Jahr: 2001
ii CO.NTE.MS
Contents
Introduction 1
1 The Geometry of oManifoIds 6
1.1 ^-Manifolds................................................................6
1.2 Exact o-Metrics............................................................9
1.3 ^-Differential Operators and the Dirac Operator Drf..........13
1.4 Geometry of the Boundary........................16
2 The o-Calculus 21
2.1 The / - and the o-Biow up........................21
2.2 Mapping Properties............................24
2.3 Composition Formula...........................27
3 Normal Operators and the Resolvent Construction 32
3.1 Symbol Map................................32
3.2 Symbolic Construction..........................33
3.3 Normal Operator at if..........................34
3.4 Inversion at if...............................36
3.5 Reduced Normal Operators at bf and ?bf................41
3.6 Inversion at ?bf..............................47
3.7 End of the Construction.........................52
3.3 Consequences...............................55
4 The Heat Kernel at Finite Time 66
4.1 (/-Heat Space and c/-Heat Calculus....................66
4.2 Composition Formula......................................................70
4.3 Normal Operators and Construction of the Heat Kernel........75
5 Rescaled d-Heat Calculus 81
5.1 The Double RescaHng ..........................81
5.2 The Rescaled Calculus and Normal Operators............. 89
5.3 The Rescaled Heat Kernel and the Index................ 97
5.4 The Signature Operator S........................101
A Appendix 107
A.l Clifford Algebra Conventions.......................107
A.2 Dirac Operator and Conformal Transformations............109
A.3 Geometry of Fibre Bundles........................HO
A.4 Mehler s Formula and the Simple Heat Space.................
A.5 Heat Kernels of Vertical Families......................
A.6 Conormal Functions, Puilbacks and Pushfonvards......... 219
References ^23
|
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| author | Vaillant, Boris |
| author_facet | Vaillant, Boris |
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| classification_rvk | SI 180 |
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| ctrlnum | (OCoLC)52664982 (DE-599)BVBBV014615866 |
| discipline | Mathematik |
| format | Thesis Book |
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| indexdate | 2024-07-09T19:04:26Z |
| institution | BVB |
| language | English |
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| spelling | Vaillant, Boris Verfasser aut Index- and spectral theory for manifolds with generalized fibred cusps vorgelegt von Boris Vaillant Bonn [Math.-Naturwiss. Fak. der Univ.] 2001 124 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Bonner mathematische Schriften 344 Bonn, Univ., Diss., 2001 Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Dirac-Operator (DE-588)4150118-4 gnd rswk-swf Faserbündel (DE-588)4135582-9 gnd rswk-swf Indextheorie (DE-588)4161489-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Dirac-Operator (DE-588)4150118-4 s Faserbündel (DE-588)4135582-9 s DE-604 Mannigfaltigkeit (DE-588)4037379-4 s Indextheorie (DE-588)4161489-6 s Spektraltheorie (DE-588)4116561-5 s Bonner mathematische Schriften 344 (DE-604)BV000001610 344 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009935649&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vaillant, Boris Index- and spectral theory for manifolds with generalized fibred cusps Bonner mathematische Schriften Spektraltheorie (DE-588)4116561-5 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Dirac-Operator (DE-588)4150118-4 gnd Faserbündel (DE-588)4135582-9 gnd Indextheorie (DE-588)4161489-6 gnd |
| subject_GND | (DE-588)4116561-5 (DE-588)4037379-4 (DE-588)4150118-4 (DE-588)4135582-9 (DE-588)4161489-6 (DE-588)4113937-9 |
| title | Index- and spectral theory for manifolds with generalized fibred cusps |
| title_auth | Index- and spectral theory for manifolds with generalized fibred cusps |
| title_exact_search | Index- and spectral theory for manifolds with generalized fibred cusps |
| title_full | Index- and spectral theory for manifolds with generalized fibred cusps vorgelegt von Boris Vaillant |
| title_fullStr | Index- and spectral theory for manifolds with generalized fibred cusps vorgelegt von Boris Vaillant |
| title_full_unstemmed | Index- and spectral theory for manifolds with generalized fibred cusps vorgelegt von Boris Vaillant |
| title_short | Index- and spectral theory for manifolds with generalized fibred cusps |
| title_sort | index and spectral theory for manifolds with generalized fibred cusps |
| topic | Spektraltheorie (DE-588)4116561-5 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Dirac-Operator (DE-588)4150118-4 gnd Faserbündel (DE-588)4135582-9 gnd Indextheorie (DE-588)4161489-6 gnd |
| topic_facet | Spektraltheorie Mannigfaltigkeit Dirac-Operator Faserbündel Indextheorie Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009935649&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001610 |
| work_keys_str_mv | AT vaillantboris indexandspectraltheoryformanifoldswithgeneralizedfibredcusps |