Topology of closed one-forms:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2004]
|
| Series: | Mathematical surveys and monographs
volume 108 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xi, 246 Seiten Illustrationen, Diagramme |
| ISBN: | 0821835319 9780821835319 |
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MARC
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| 100 | 1 | |a Farber, Michael |e Verfasser |0 (DE-588)1153432862 |4 aut | |
| 245 | 1 | 0 | |a Topology of closed one-forms |c Michael Farber |
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| 264 | 4 | |c © 2004 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface vii
Chapter 1. The Novikov Numbers 1
1.1. Homological algebra of Morse inequalities 1
1.2. The Novikov ring Nov(r) 6
1.3. The rational subring TZ(r) 9
1.4. Homology of local coefficient systems 12
1.5. The Novikov numbers 17
1.6. Further properties of the Novikov numbers 21
1.7. Novikov numbers and Betti numbers of flat line bundles 30
Chapter 2. The Novikov Inequalities 35
2.1. Closed 1 forms 35
2.2. Geometry of Novikov theory 38
2.3. The Novikov inequalities 45
Chapter 3. The Universal Complex 49
3.1. The Main Theorem 49
3.2. Line bundles and algebraic integers 54
3.3. Generic flat vector bundles 56
3.4. Examples 58
Chapter 4. Construction of the Universal Complex 61
4.1. Chain collapse 61
4.2. Proof of Theorem 3.1 in the rank 1 case 63
4.3. Proof of Theorem 3.1 in the general case 66
4.4. Refined universal complex and deformation complex 75
Chapter 5. Bott type Inequalities 81
5.1. Topology of the set of zeros 81
5.2. Proofs of Theorems 5.1 and 5.5 86
Chapter 6. Inequalities with Von Neumann Betti Numbers 91
Chapter 7. Equivariant Theory 99
7.1. Basic 1 forms 100
7.2. Equivariant Novikov inequalities 101
7.3. Application: Fixed points of a symplectic circle action 104
7.4. Signature via Novikov numbers 108
Chapter 8. Exactness of the Novikov Inequalities 113
8.1. Exactness Theorem 113
V
vi CONTENTS
8.2. Finiteness theorem for codimension two knots 114
8.3. Surgery on codimension one submanifolds 115
8.4. Algebra of minimal lattices 119
8.5. Proof of The Exactness Theorem 122
Chapter 9. Morse Theory of Harmonic Forms 125
9.1. Topology of singular foliations of closed 1 forms 125
9.2. Intrinsically harmonic 1 forms 131
9.3. Examples of singular foliations 137
9.4. Proof of Calabi s Theorem 140
9.5. Morse numbers of harmonic 1 forms 147
Chapter 10. Lusternik Schnirelman Theory, Closed 1 Forms,
and Dynamics 159
10.1. Colliding the critical points 160
10.2. Closed 1 forms on topological spaces 162
10.3. Category of a space with respect to a cohomology class 165
10.4. Estimate of the number of zeros 170
10.5. Gradient convex neighborhoods 177
10.6. Movable homology classes 179
10.7. Cohomological lower bound for cat(X, £) 181
10.8. Deformations and their spectral sequences 184
10.9. Families of fiat bundles and higher Massey products 190
10.10. Estimate for cat(X, £) in terms of ^ survivors 194
10.11. Flows, Lyapunov 1 forms and asymptotic cycles 197
Appendix A. Manifolds with Corners 205
Appendix B. Morse Bott Functions on Manifolds with Corners 213
Appendix C. Morse Bott Inequalities 227
Appendix D. Relative Morse Theory 233
Bibliography 239
Index 245
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:59:23Z |
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| isbn | 0821835319 9780821835319 |
| language | English |
| lccn | 2003062825 |
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| publishDate | 2004 |
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| series2 | Mathematical surveys and monographs |
| spelling | Farber, Michael Verfasser (DE-588)1153432862 aut Topology of closed one-forms Michael Farber Providence, Rhode Island American Mathematical Society [2004] © 2004 xi, 246 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs volume 108 Análise global larpcal Análise matemática larpcal Feuilletages (Mathématiques) Folheações larpcal Points critiques, Théorie des (Analyse mathématique) Topologia diferencial larpcal Topologie différentielle Critical point theory (Mathematical analysis) Differential topology Foliations (Mathematics) Differentialform (DE-588)4149772-7 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Differentialform (DE-588)4149772-7 s Topologie (DE-588)4060425-1 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1335-4 Mathematical surveys and monographs volume 108 (DE-604)BV000018014 108 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012860852&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Farber, Michael Topology of closed one-forms Mathematical surveys and monographs Análise global larpcal Análise matemática larpcal Feuilletages (Mathématiques) Folheações larpcal Points critiques, Théorie des (Analyse mathématique) Topologia diferencial larpcal Topologie différentielle Critical point theory (Mathematical analysis) Differential topology Foliations (Mathematics) Differentialform (DE-588)4149772-7 gnd Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4149772-7 (DE-588)4060425-1 |
| title | Topology of closed one-forms |
| title_auth | Topology of closed one-forms |
| title_exact_search | Topology of closed one-forms |
| title_full | Topology of closed one-forms Michael Farber |
| title_fullStr | Topology of closed one-forms Michael Farber |
| title_full_unstemmed | Topology of closed one-forms Michael Farber |
| title_short | Topology of closed one-forms |
| title_sort | topology of closed one forms |
| topic | Análise global larpcal Análise matemática larpcal Feuilletages (Mathématiques) Folheações larpcal Points critiques, Théorie des (Analyse mathématique) Topologia diferencial larpcal Topologie différentielle Critical point theory (Mathematical analysis) Differential topology Foliations (Mathematics) Differentialform (DE-588)4149772-7 gnd Topologie (DE-588)4060425-1 gnd |
| topic_facet | Análise global Análise matemática Feuilletages (Mathématiques) Folheações Points critiques, Théorie des (Analyse mathématique) Topologia diferencial Topologie différentielle Critical point theory (Mathematical analysis) Differential topology Foliations (Mathematics) Differentialform Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012860852&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT farbermichael topologyofclosedoneforms |