Monopoles and three-manifolds:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2007
|
| Edition: | 1. publ. |
| Series: | New mathematical monographs
10 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| ISBN: | 9780521880220 9780521184762 |
Staff View
MARC
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| 100 | 1 | |a Kronheimer, Peter B. |e Verfasser |0 (DE-588)17219802X |4 aut | |
| 245 | 1 | 0 | |a Monopoles and three-manifolds |c Peter Kronheimer ; Tomasz Mrowka |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2007 | |
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| 490 | 1 | |a New mathematical monographs |v 10 | |
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| 650 | 4 | |a Homology theory | |
| 650 | 4 | |a Moduli theory | |
| 650 | 4 | |a Seiberg-Witten invariants | |
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Record in the Search Index
| _version_ | 1804137104316301312 |
|---|---|
| adam_text | Contents
Preface
page
xi
I Outlines
1
1 Monopole
invariants of four-manifolds
2
2
Morse theory
14
3 Monopole
Floer homology
for three-manifolds
49
Notes and references for Chapter
1 82
II The Seiberg-
Witten
equations and compactness
84
4
Basic terms
85
5
Compactness and properness
99
6
The blown-up configuration space
112
7
Unique continuation
120
8
Compactness in the blown-up configuration space
130
Notes and references for Chapter II
132
III Hubert manifolds and perturbations
134
9
Completions and Hubert manifolds
134
10
Abstract perturbations
152
11
Constructing tame perturbations
171
Notes and references for Chapter HI
194
IV Moduli spaces and transversality
195
12
Transversality for the three-dimensional equations
196
13
Moduli spaces of trajectories
217
14
Local structure of moduli spaces
239
15
Transversality for moduli spaces of trajectories
265
Notes and references for Chapter IV
272
viii
Contents
V Compactness and gluing
274
16
Compactness of trajectory spaces
275
17
The moduli space on a finite cylinder
294
18
Stable manifolds and gluing near critical points
317
19
Gluing trajectories
343
Notes and references for Chapter V
374
VI
Floer homology
375
20
Orienting moduli spaces
375
21 .
A version of Stokes theorem
405
22
Floer
homology
410
Notes and references for Chapter VI
448
VII Cobordisms
and
invariance
449
23
Summary of results
449
24
The moduli space on a manifold with boundary
461
25
Maps from cobordisms
508
26
Composing cobordisms
535
27
Closed four-manifolds
551
28
Canonical gradings
581
Notes and references for Chapter
VII
589
VIII
Non-exact perturbations
590
29
Closed two-forms as perturbations
590
30
Floer
groups and non-exact perturbations
597
31
Some isomorphisms
605
32
Applications to gluing
622
Notes and references for Chapter
VIII 633
IX Calculations
634
33
Coupled Morse theory
634
34
Calculation of coupled homology
658
35
Application to the
Floer
groups HM
678
36
The manifold 51 xS2
695
37
The three-torus
699
38
Elliptic surfaces
711
Notes and references for Chapter IX
719
Contents ix
X Further developments
721
39
Homology spheres and negative-definite cobordisms
722
40
Genus bounds and scalar curvature
733
41
Foliations and non-vanishing theorems
741
42
Surgery and exact triangles
757
Notes and references for Chapter X
778
References
779
Glossary of notation
785
Index
792
|
| adam_txt |
Contents
Preface
page
xi
I Outlines
1
1 Monopole
invariants of four-manifolds
2
2
Morse theory
14
3 Monopole
Floer homology
for three-manifolds
49
Notes and references for Chapter
1 82
II The Seiberg-
Witten
equations and compactness
84
4
Basic terms
85
5
Compactness and properness
99
6
The blown-up configuration space
112
7
Unique continuation
120
8
Compactness in the blown-up configuration space
130
Notes and references for Chapter II
132
III Hubert manifolds and perturbations
134
9
Completions and Hubert manifolds
134
10
Abstract perturbations
152
11
Constructing tame perturbations
171
Notes and references for Chapter HI
194
IV Moduli spaces and transversality
195
12
Transversality for the three-dimensional equations
196
13
Moduli spaces of trajectories
217
14
Local structure of moduli spaces
239
15
Transversality for moduli spaces of trajectories
265
Notes and references for Chapter IV
272
viii
Contents
V Compactness and gluing
274
16
Compactness of trajectory spaces
275
17
The moduli space on a finite cylinder
294
18
Stable manifolds and gluing near critical points
317
19
Gluing trajectories
343
Notes and references for Chapter V
374
VI
Floer homology
375
20
Orienting moduli spaces
375
21 .
A version of Stokes'theorem
405
22
Floer
homology
410
Notes and references for Chapter VI
448
VII Cobordisms
and
invariance
449
23
Summary of results
449
24
The moduli space on a manifold with boundary
461
25
Maps from cobordisms
508
26
Composing cobordisms
535
27
Closed four-manifolds
551
28
Canonical gradings
581
Notes and references for Chapter
VII
589
VIII
Non-exact perturbations
590
29
Closed two-forms as perturbations
590
30
Floer
groups and non-exact perturbations
597
31
Some isomorphisms
605
32
Applications to gluing
622
Notes and references for Chapter
VIII 633
IX Calculations
634
33
Coupled Morse theory
634
34
Calculation of coupled homology
658
35
Application to the
Floer
groups HM
678
36
The manifold 51 xS2
695
37
The three-torus
699
38
Elliptic surfaces
711
Notes and references for Chapter IX
719
Contents ix
X Further developments
721
39
Homology spheres and negative-definite cobordisms
722
40
Genus bounds and scalar curvature
733
41
Foliations and non-vanishing theorems
741
42
Surgery and exact triangles
757
Notes and references for Chapter X
778
References
779
Glossary of notation
785
Index
792 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T18:41:11Z |
| indexdate | 2024-07-09T21:06:59Z |
| institution | BVB |
| isbn | 9780521880220 9780521184762 |
| language | English |
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| spelling | Kronheimer, Peter B. Verfasser (DE-588)17219802X aut Monopoles and three-manifolds Peter Kronheimer ; Tomasz Mrowka 1. publ. Cambridge Cambridge Univ. Press 2007 txt rdacontent n rdamedia nc rdacarrier New mathematical monographs 10 Hier auch später erschienene, unveränderte Nachdrucke Homology theory Moduli theory Seiberg-Witten invariants Three-manifolds (Topology) Dimension 3 (DE-588)4321722-9 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Dimension 3 (DE-588)4321722-9 s Algebraische Topologie (DE-588)4120861-4 s DE-604 Mrowka, Tomasz Verfasser aut New mathematical monographs 10 (DE-604)BV035420183 10 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016029680&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kronheimer, Peter B. Mrowka, Tomasz Monopoles and three-manifolds New mathematical monographs Homology theory Moduli theory Seiberg-Witten invariants Three-manifolds (Topology) Dimension 3 (DE-588)4321722-9 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4321722-9 (DE-588)4037379-4 (DE-588)4120861-4 |
| title | Monopoles and three-manifolds |
| title_auth | Monopoles and three-manifolds |
| title_exact_search | Monopoles and three-manifolds |
| title_exact_search_txtP | Monopoles and three-manifolds |
| title_full | Monopoles and three-manifolds Peter Kronheimer ; Tomasz Mrowka |
| title_fullStr | Monopoles and three-manifolds Peter Kronheimer ; Tomasz Mrowka |
| title_full_unstemmed | Monopoles and three-manifolds Peter Kronheimer ; Tomasz Mrowka |
| title_short | Monopoles and three-manifolds |
| title_sort | monopoles and three manifolds |
| topic | Homology theory Moduli theory Seiberg-Witten invariants Three-manifolds (Topology) Dimension 3 (DE-588)4321722-9 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | Homology theory Moduli theory Seiberg-Witten invariants Three-manifolds (Topology) Dimension 3 Mannigfaltigkeit Algebraische Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016029680&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035420183 |
| work_keys_str_mv | AT kronheimerpeterb monopolesandthreemanifolds AT mrowkatomasz monopolesandthreemanifolds |