Loop spaces, characteristic classes and geometric quantization:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2008
|
| Edition: | Reprint of the 1993 ed. |
| Series: | Modern Birkhäuser classics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 300 S. |
| ISBN: | 9780817647308 9780817647315 |
Staff View
MARC
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| 100 | 1 | |a Brylinski, Jean-Luc |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Loop spaces, characteristic classes and geometric quantization |c Jean-Luc Brylinski |
| 250 | |a Reprint of the 1993 ed. | ||
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2008 | |
| 300 | |a XVI, 300 S. | ||
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| 650 | 4 | |a Homology theory | |
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Record in the Search Index
| _version_ | 1804137716944732160 |
|---|---|
| adam_text | Table
of
Contents
Introduction
...........................................................ix
I. Complexes of Sheaves and Their Cohomology
1.
Injective resolutions and sheaf cohomology
.......................1
2.
Spectral sequences and complexes of sheaves
....................13
3.
Čech
cohomology and hypercohomology
.........................24
4.
de Rham
cohomology
...........................................34
5.
Deligne and Cheeger-Simons cohomologies
.......................46
6.
The Leray spectral sequence
....................................54
II. Line Bundles and Geometric Quantization
1.
Classification of line bundles
....................................62
2.
Line bundles with connection
...................................70
3.
Central extension of the Lie algebra of hamiltonian vector fields
. 85
4.
Central extension of a group of symplectic diffeomorphisms
.....94
5.
Generalizations of Kostant s central extension
..................103
III.
Kahler
Geometry of the Space of Knots
1.
The space of singular knots
....................................110
2.
Topology of the space of singular knots
........................115
3.
Tautological principal bundles
.................................121
4.
The complex structure
........................................126
5.
The symplectic structure
.......................................135
6.
The riemannian structure
......................................144
7.
The group of unimodular diffeomorphisms
......................152
IV. Degree
3
Cohomology: The Dixmier-Douady Theory
1.
Infinite-dimensional algebra bundles
............................158
2.
Connections and curvature
.....................................168
3.
Examples of
projective
Hubert space bundles
...................175
V. Degree
3
Cohomology: Sheaves of Groupoids
1.
Descent theory for sheaves
.....................................182
2.
Sheaves of groupoids and
gerbes
...............................191
3.
Differential geometry of
gerbes
................................205
4.
The canonical sheaf of groupoids on a compact Lie group
......219
5.
Examples of sheaves of groupoids
.............................228
VT. Line
Bundles over Loop Spaces
1.
Holonomy of line bundles
.....................................234
2.
Construction of the line bundle
................................236
3.
The line bundle on the space of knots
.........................243
4.
Central extension of loop groups
..............................247
5.
Relation with smooth Deligne cohomology
.....................250
6.
Parallel transport for sheaves of groupoids
.....................254
VII.
The Dirac
Monopole
1.
Dirac s construction
...........................................257
2.
The sheaf of groupoids over S3
................................264
3.
Obstruction to
5í7(2)-equivariance
............................268
Bibliography
.........................................................278
List of Notations
.....................................................286
Index
................................................................295
|
| adam_txt |
Table
of
Contents
Introduction
.ix
I. Complexes of Sheaves and Their Cohomology
1.
Injective resolutions and sheaf cohomology
.1
2.
Spectral sequences and complexes of sheaves
.13
3.
Čech
cohomology and hypercohomology
.24
4.
de Rham
cohomology
.34
5.
Deligne and Cheeger-Simons cohomologies
.46
6.
The Leray spectral sequence
.54
II. Line Bundles and Geometric Quantization
1.
Classification of line bundles
.62
2.
Line bundles with connection
.70
3.
Central extension of the Lie algebra of hamiltonian vector fields
. 85
4.
Central extension of a group of symplectic diffeomorphisms
.94
5.
Generalizations of Kostant's central extension
.103
III.
Kahler
Geometry of the Space of Knots
1.
The space of singular knots
.110
2.
Topology of the space of singular knots
.115
3.
Tautological principal bundles
.121
4.
The complex structure
.126
5.
The symplectic structure
.135
6.
The riemannian structure
.144
7.
The group of unimodular diffeomorphisms
.152
IV. Degree
3
Cohomology: The Dixmier-Douady Theory
1.
Infinite-dimensional algebra bundles
.158
2.
Connections and curvature
.168
3.
Examples of
projective
Hubert space bundles
.175
V. Degree
3
Cohomology: Sheaves of Groupoids
1.
Descent theory for sheaves
.182
2.
Sheaves of groupoids and
gerbes
.191
3.
Differential geometry of
gerbes
.205
4.
The canonical sheaf of groupoids on a compact Lie group
.219
5.
Examples of sheaves of groupoids
.228
VT. Line
Bundles over Loop Spaces
1.
Holonomy of line bundles
.234
2.
Construction of the line bundle
.236
3.
The line bundle on the space of knots
.243
4.
Central extension of loop groups
.247
5.
Relation with smooth Deligne cohomology
.250
6.
Parallel transport for sheaves of groupoids
.254
VII.
The Dirac
Monopole
1.
Dirac's construction
.257
2.
The sheaf of groupoids over S3
.264
3.
Obstruction to
5í7(2)-equivariance
.268
Bibliography
.278
List of Notations
.286
Index
.295 |
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| edition | Reprint of the 1993 ed. |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:07:17Z |
| indexdate | 2024-07-09T21:16:43Z |
| institution | BVB |
| isbn | 9780817647308 9780817647315 |
| language | English |
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| physical | XVI, 300 S. |
| publishDate | 2008 |
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| publisher | Birkhäuser |
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| spelling | Brylinski, Jean-Luc Verfasser aut Loop spaces, characteristic classes and geometric quantization Jean-Luc Brylinski Reprint of the 1993 ed. Boston [u.a.] Birkhäuser 2008 XVI, 300 S. txt rdacontent n rdamedia nc rdacarrier Modern Birkhäuser classics Characteristic classes Homology theory Loop spaces Kohomologie (DE-588)4031700-6 gnd rswk-swf Charakteristische Klasse (DE-588)4194231-0 gnd rswk-swf Schleifenraum (DE-588)4179711-5 gnd rswk-swf Geometrische Quantisierung (DE-588)4156720-1 gnd rswk-swf Geradenbündel (DE-588)4156783-3 gnd rswk-swf Garbe Mathematik (DE-588)4019261-1 gnd rswk-swf Charakteristische Klasse (DE-588)4194231-0 s Garbe Mathematik (DE-588)4019261-1 s DE-604 Kohomologie (DE-588)4031700-6 s Geradenbündel (DE-588)4156783-3 s Schleifenraum (DE-588)4179711-5 s Geometrische Quantisierung (DE-588)4156720-1 s Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016539983&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brylinski, Jean-Luc Loop spaces, characteristic classes and geometric quantization Characteristic classes Homology theory Loop spaces Kohomologie (DE-588)4031700-6 gnd Charakteristische Klasse (DE-588)4194231-0 gnd Schleifenraum (DE-588)4179711-5 gnd Geometrische Quantisierung (DE-588)4156720-1 gnd Geradenbündel (DE-588)4156783-3 gnd Garbe Mathematik (DE-588)4019261-1 gnd |
| subject_GND | (DE-588)4031700-6 (DE-588)4194231-0 (DE-588)4179711-5 (DE-588)4156720-1 (DE-588)4156783-3 (DE-588)4019261-1 |
| title | Loop spaces, characteristic classes and geometric quantization |
| title_auth | Loop spaces, characteristic classes and geometric quantization |
| title_exact_search | Loop spaces, characteristic classes and geometric quantization |
| title_exact_search_txtP | Loop spaces, characteristic classes and geometric quantization |
| title_full | Loop spaces, characteristic classes and geometric quantization Jean-Luc Brylinski |
| title_fullStr | Loop spaces, characteristic classes and geometric quantization Jean-Luc Brylinski |
| title_full_unstemmed | Loop spaces, characteristic classes and geometric quantization Jean-Luc Brylinski |
| title_short | Loop spaces, characteristic classes and geometric quantization |
| title_sort | loop spaces characteristic classes and geometric quantization |
| topic | Characteristic classes Homology theory Loop spaces Kohomologie (DE-588)4031700-6 gnd Charakteristische Klasse (DE-588)4194231-0 gnd Schleifenraum (DE-588)4179711-5 gnd Geometrische Quantisierung (DE-588)4156720-1 gnd Geradenbündel (DE-588)4156783-3 gnd Garbe Mathematik (DE-588)4019261-1 gnd |
| topic_facet | Characteristic classes Homology theory Loop spaces Kohomologie Charakteristische Klasse Schleifenraum Geometrische Quantisierung Geradenbündel Garbe Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016539983&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT brylinskijeanluc loopspacescharacteristicclassesandgeometricquantization |