J-holomorphic curves and quantum cohomology:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
1994
|
| Schriftenreihe: | University lecture series
Volume 6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | vii, 209 Seiten |
| ISBN: | 0821803328 9780821803325 |
Internformat
MARC
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| 100 | 1 | |a McDuff, Dusa |d 1945- |e Verfasser |0 (DE-588)172795176 |4 aut | |
| 245 | 1 | 0 | |a J-holomorphic curves and quantum cohomology |c Dusa McDuff ; Dietmar Salamon |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c 1994 | |
| 264 | 4 | |c © 1994 | |
| 300 | |a vii, 209 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a University lecture series |v Volume 6 | |
| 650 | 7 | |a Fonctions holomorphes |2 ram | |
| 650 | 7 | |a Homologie |2 ram | |
| 650 | 7 | |a Variétés symplectiques |2 ram | |
| 650 | 4 | |a Holomorphic functions | |
| 650 | 4 | |a Homology theory | |
| 650 | 4 | |a Symplectic manifolds | |
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| 689 | 1 | 1 | |a Kohomologie |0 (DE-588)4031700-6 |D s |
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| 700 | 1 | |a Salamon, Dietmar |d 1953- |e Verfasser |0 (DE-588)1015895271 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804124565311324160 |
|---|---|
| adam_text | Contents
1 Introduction 1
1.1 Symplectic manifolds 1
1.2 J holomorphic curves 3
1.3 Moduli spaces 4
1.4 Compactness 5
1.5 Evaluation maps 6
1.6 The Gromov Witten invariants 8
1.7 Quantum cohomology 9
1.8 Novikov rings and Floer homology 11
2 Local Behaviour 13
2.1 The generalised Cauchy Riemann equation 13
2.2 Critical points 15
2.3 Somewhere injective curves 18
3 Moduli Spaces and Transversality 23
3.1 The main theorems 23
3.2 Elliptic regularity 25
3.3 Implicit function theorem 27
3.4 Transversality 33
3.5 A regularity criterion 37
4 Compactness 41
4.1 Energy 42
4.2 Removal of Singularities 43
4.3 Bubbling 46
4.4 Gromov compactness 50
4.5 Proof of Gromov compactness 52
5 Compactification of Moduli Spaces 59
5.1 Semi positivity 59
5.2 The image of the evaluation map 61
5.3 The image of the p fold evaluation map 65
5.4 The evaluation map for marked curves 66
v
vi CONTENTS
6 Evaluation Maps and Transversality 71
6.1 Evaluation maps are submersions 71
6.2 Moduli spaces of iV tuples of curves 74
6.3 Moduli spaces of cusp curves 75
6.4 Evaluation maps for cusp curves 79
6.5 Proofs of the theorems in Sections 5.2 and 5.3 81
6.6 Proof of the theorem in Section 5.4 83
7 Gromov Witten Invariants 89
7.1 Pseudo cycles 90
7.2 The invariant $ 92
7.3 Examples 97
7.4 The invariant * 100
8 Quantum Cohomology 105
8.1 Witten s deformed cohomology ring 105
8.2 Associativity and composition rules 112
8.3 Flag manifolds 117
8.4 Grassmannians 121
8.5 The Gromov Witten potential 129
9 Novikov Rings and Calabi Yau Manifolds 139
9.1 Multiply covered curves 140
9.2 Novikov rings 142
9.3 Calabi Yau manifolds 146
10 Floer Homology 151
10.1 Floer s cochain complex 151
10.2 Ring structure 157
10.3 A comparison theorem 158
10.4 Donaldson s quantum category 159
10.5 Closing remark 163
A Gluing 165
A.I Cutoff functions 166
A.2 Connected sums of J holomorphic curves 168
A.3 Weighted norms 169
A.4 An estimate for the inverse 171
A.5 Gluing 174
B Elliptic Regularity 179
B.I Sobolev spaces 179
B.2 The Calderon Zygmund inequality 183
B.3 Cauchy Riemann operators 188
B.4 Elliptic bootstrapping 190
Bibliography 195
Indexes 201
|
| any_adam_object | 1 |
| author | McDuff, Dusa 1945- Salamon, Dietmar 1953- |
| author_GND | (DE-588)172795176 (DE-588)1015895271 |
| author_facet | McDuff, Dusa 1945- Salamon, Dietmar 1953- |
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| callnumber-first | Q - Science |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 165 SK 240 SK 320 |
| ctrlnum | (OCoLC)30666918 (DE-599)BVBBV010169030 |
| dewey-full | 516.3/62 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/62 |
| dewey-search | 516.3/62 |
| dewey-sort | 3516.3 262 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010169030 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:47:41Z |
| institution | BVB |
| isbn | 0821803328 9780821803325 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006753818 |
| oclc_num | 30666918 |
| open_access_boolean | |
| owner | DE-703 DE-12 DE-355 DE-BY-UBR DE-384 DE-739 DE-29T DE-19 DE-BY-UBM DE-11 DE-188 |
| owner_facet | DE-703 DE-12 DE-355 DE-BY-UBR DE-384 DE-739 DE-29T DE-19 DE-BY-UBM DE-11 DE-188 |
| physical | vii, 209 Seiten |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | University lecture series |
| series2 | University lecture series |
| spelling | McDuff, Dusa 1945- Verfasser (DE-588)172795176 aut J-holomorphic curves and quantum cohomology Dusa McDuff ; Dietmar Salamon Providence, Rhode Island American Mathematical Society 1994 © 1994 vii, 209 Seiten txt rdacontent n rdamedia nc rdacarrier University lecture series Volume 6 Fonctions holomorphes ram Homologie ram Variétés symplectiques ram Holomorphic functions Homology theory Symplectic manifolds Kohomologie (DE-588)4031700-6 gnd rswk-swf Holomorphe Kurve (DE-588)4160476-3 gnd rswk-swf Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd rswk-swf Holomorphe Kurve (DE-588)4160476-3 s Kohomologie (DE-588)4031700-6 s DE-604 Symplektische Mannigfaltigkeit (DE-588)4290704-4 s Salamon, Dietmar 1953- Verfasser (DE-588)1015895271 aut University lecture series Volume 6 (DE-604)BV004153846 6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006753818&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | McDuff, Dusa 1945- Salamon, Dietmar 1953- J-holomorphic curves and quantum cohomology University lecture series Fonctions holomorphes ram Homologie ram Variétés symplectiques ram Holomorphic functions Homology theory Symplectic manifolds Kohomologie (DE-588)4031700-6 gnd Holomorphe Kurve (DE-588)4160476-3 gnd Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd |
| subject_GND | (DE-588)4031700-6 (DE-588)4160476-3 (DE-588)4290704-4 |
| title | J-holomorphic curves and quantum cohomology |
| title_auth | J-holomorphic curves and quantum cohomology |
| title_exact_search | J-holomorphic curves and quantum cohomology |
| title_full | J-holomorphic curves and quantum cohomology Dusa McDuff ; Dietmar Salamon |
| title_fullStr | J-holomorphic curves and quantum cohomology Dusa McDuff ; Dietmar Salamon |
| title_full_unstemmed | J-holomorphic curves and quantum cohomology Dusa McDuff ; Dietmar Salamon |
| title_short | J-holomorphic curves and quantum cohomology |
| title_sort | j holomorphic curves and quantum cohomology |
| topic | Fonctions holomorphes ram Homologie ram Variétés symplectiques ram Holomorphic functions Homology theory Symplectic manifolds Kohomologie (DE-588)4031700-6 gnd Holomorphe Kurve (DE-588)4160476-3 gnd Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd |
| topic_facet | Fonctions holomorphes Homologie Variétés symplectiques Holomorphic functions Homology theory Symplectic manifolds Kohomologie Holomorphe Kurve Symplektische Mannigfaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006753818&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004153846 |
| work_keys_str_mv | AT mcduffdusa jholomorphiccurvesandquantumcohomology AT salamondietmar jholomorphiccurvesandquantumcohomology |