Elliptic operators, topology and asymptotic methods:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Reaton [u.a.]
Chapman & Hall
2001
|
| Edition: | 2. ed., 1. CRC reprint |
| Series: | Chapman & Hall CRC research notes in mathematics
395 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 203 - 206 |
| Physical Description: | 209 S. |
| ISBN: | 0582325021 9780582325029 |
Staff View
MARC
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| 100 | 1 | |a Roe, John |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Elliptic operators, topology and asymptotic methods |c John Roe |
| 250 | |a 2. ed., 1. CRC reprint | ||
| 264 | 1 | |a Boca Reaton [u.a.] |b Chapman & Hall |c 2001 | |
| 300 | |a 209 S. | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Chapman & Hall CRC research notes in mathematics |v 395 | |
| 500 | |a Literaturverz. S. 203 - 206 | ||
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Record in the Search Index
| _version_ | 1804139320084267009 |
|---|---|
| adam_text | Contents
Chapter
1.
Resumé
of Riemannian geometry
9
Connections
9
Riemannian geometry
12
Differential forms
17
Exercises
21
Chapter
2.
Connections, curvature, and characteristic classes
23
Principal bundles and their connections
23
Characteristic classes
29
Genera
34
Notes
37
Exercises
37
Chapter
3.
Clifford algebras and Dirac operators
41
Clifford bundles and Dirac operators
41
Clifford bundles and curvature
46
Examples of Clifford bundles
49
Notes
52
Exercises
53
Chapter
4.
The Spin groups
55
The Clifford algebra as a superalgebra
55
Groups of invertibles in the Clifford algebra
57
Representation theory of the Clifford algebra
59
Spin structures on manifolds
62
Spin bundles and characteristic classes
64
The complex Spin group
67
Notes
68
Exercises
68
Chapter
5.
Analytic properties of Dirac operators
71
3
Sobolev
Spaces
Analysis
of the Dirac operator
The functional calculus
Notes
Exercises
Chapter
6.
Hodge theory
Notes
Exercises
71
75
82
84
84
87
91
92
Chapter
7.
The heat and wave equations
95
Existence and uniqueness theorems
9õ
The asymptotic expansion for the heat kernel
99
Finite propagation speed for the wave equation
104
Notes
107
Exercises
108
Chapter
8.
Traces and eigenvalue asymptotics
109
Eigenvalue growth
109
Trace-class operators
110
Weyľs
asymptotic formula
114
Notes
117
Exercises
117
Chapter
9.
Some non-compact manifolds
119
The harmonic oscillator
119
Witten s perturbation of the
de Rham
complex
125
Functional calculus on open manifolds
127
Notes
130
Exercises
130
Chapter
10.
The Lefschetz formula
133
Lefschetz numbers
133
The fixed-point contributions
136
Notes
140
Exercises
140
Chapter
11.
The index problem
141
Gradings and Clifford bundles
141
Graded Dirac operators
143
The heat equation and the index theorem
147
Notes
148
Exorcises
149
Chapter
12.
The Getzler calculus and the local index theorem
151
Filtered algebras and symbols
151
Getzler symbols
154
The Getzler symbol of the heat kernel
157
The exact solution
162
The index theorem
164
Notes
165
Exercises
166
Chapter
13.
Applications of the index theorem
169
The spinor Dirac operator
169
The signature theorem
172
The Hirzebruch-Riemann-Roch theorem
175
Local index theory
177
Notes
179
Exercises
180
Chapter
14.
Witten s approach to Morse theory
183
The Morse inequalities
183
Morse functions
185
The contribution from the critical points
189
Notes
192
Chapter
15.
Atiyah s
Г
-index
theorem
193
An algebra of smoothing operators
193
Renormalized dimensions and the index theorem
198
Notes
201
References
203
|
| any_adam_object | 1 |
| author | Roe, John |
| author_facet | Roe, John |
| author_role | aut |
| author_sort | Roe, John |
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| building | Verbundindex |
| bvnumber | BV035639771 |
| classification_rvk | SI 880 SK 620 |
| ctrlnum | (OCoLC)635240262 (DE-599)BVBBV035639771 |
| discipline | Mathematik |
| edition | 2. ed., 1. CRC reprint |
| format | Book |
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| id | DE-604.BV035639771 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:42:12Z |
| institution | BVB |
| isbn | 0582325021 9780582325029 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017694583 |
| oclc_num | 635240262 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-11 DE-83 |
| owner_facet | DE-355 DE-BY-UBR DE-11 DE-83 |
| physical | 209 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Chapman & Hall |
| record_format | marc |
| series | Chapman & Hall CRC research notes in mathematics |
| series2 | Chapman & Hall CRC research notes in mathematics |
| spelling | Roe, John Verfasser aut Elliptic operators, topology and asymptotic methods John Roe 2. ed., 1. CRC reprint Boca Reaton [u.a.] Chapman & Hall 2001 209 S. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall CRC research notes in mathematics 395 Literaturverz. S. 203 - 206 Asymptotische Entwicklung (DE-588)4112609-9 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Indextheorem (DE-588)4140055-0 gnd rswk-swf Elliptischer Differentialoperator (DE-588)4140057-4 gnd rswk-swf Elliptischer Differentialoperator (DE-588)4140057-4 s Topologie (DE-588)4060425-1 s Asymptotische Entwicklung (DE-588)4112609-9 s DE-604 Indextheorem (DE-588)4140055-0 s Chapman & Hall CRC research notes in mathematics 395 (DE-604)BV012456897 395 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017694583&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roe, John Elliptic operators, topology and asymptotic methods Chapman & Hall CRC research notes in mathematics Asymptotische Entwicklung (DE-588)4112609-9 gnd Topologie (DE-588)4060425-1 gnd Indextheorem (DE-588)4140055-0 gnd Elliptischer Differentialoperator (DE-588)4140057-4 gnd |
| subject_GND | (DE-588)4112609-9 (DE-588)4060425-1 (DE-588)4140055-0 (DE-588)4140057-4 |
| title | Elliptic operators, topology and asymptotic methods |
| title_auth | Elliptic operators, topology and asymptotic methods |
| title_exact_search | Elliptic operators, topology and asymptotic methods |
| title_full | Elliptic operators, topology and asymptotic methods John Roe |
| title_fullStr | Elliptic operators, topology and asymptotic methods John Roe |
| title_full_unstemmed | Elliptic operators, topology and asymptotic methods John Roe |
| title_short | Elliptic operators, topology and asymptotic methods |
| title_sort | elliptic operators topology and asymptotic methods |
| topic | Asymptotische Entwicklung (DE-588)4112609-9 gnd Topologie (DE-588)4060425-1 gnd Indextheorem (DE-588)4140055-0 gnd Elliptischer Differentialoperator (DE-588)4140057-4 gnd |
| topic_facet | Asymptotische Entwicklung Topologie Indextheorem Elliptischer Differentialoperator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017694583&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV012456897 |
| work_keys_str_mv | AT roejohn ellipticoperatorstopologyandasymptoticmethods |