Frobenius manifolds, quantum cohomology and moduli spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
AMS
1999
|
| Series: | American Mathematical Society: Colloquium publications
47 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 303 S. |
| ISBN: | 0821819178 |
Staff View
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| 245 | 1 | 0 | |a Frobenius manifolds, quantum cohomology and moduli spaces |c Yuri I. Manin |
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Record in the Search Index
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| adam_text | Contents
Preface xi
Chapter 0. Introduction: What Is Quantum Cohomology? 1
Chapter I. Introduction to Frobenius Manifolds 17
§1. Definition of Frobenius manifolds and the structure connection 17
§2. Identity, Euler field, and the extended structure connection 22
§3. Semisimple Frobenius manifolds 27
§4. Examples 35
§5. Weak Frobenius manifolds 42
Chapter II. Frobenius Manifolds and Isomonodromic Deformations 49
§1. The second structure connection 49
§2. Isomonodromic deformations 55
§3. Semisimple Frobenius manifolds as special solutions to the Schlesinger
equations 60
§4. Quantum cohomology of projective spaces 66
§5. Dimension three and Painleve VI 71
Chapter III. Frobenius Manifolds and Moduli Spaces of Curves 83
§1. Formal Frobenius manifolds and Comm^ algebras 83
§2. Pointed curves and their graphs 88
§3. Moduli spaces of genus 0 91
§4. Formal Frobenius manifolds and Cohomological Field Theories 99
§5. Gromov Witten invariants and quantum cohomology: Axiomatic
theory 115
§6. Formal Frobenius manifolds of rank one and Weil Petersson vol¬
umes of moduli spaces 121
§7. Tensor product of analytic Frobenius manifolds 134
§8. K. Saito s frameworks and singularities 146
§9. Maurer Cartan equations and Gerstenhaber Batalin Vilkovyski
algebras 157
§10. From dGBV algebras to Frobenius manifolds 168
Chapter IV. Operads, Graphs, and Perturbation Series 175
§1. Classical linear operads 175
§2. Operads and graphs 184
§3. Sums over graphs 187
§4. Generating functions 193
ix
x CONTENTS
Chapter V. Stable Maps, Stacks, and Chow Groups 201
§1. Prestable curves and prestable maps 201
§2. Flat families of curves and maps 206
§3. Groupoids and moduli groupoids 210
§4. Morphisms of groupoids and moduli groupoids 213
§5. Stacks 219
§6. Homological Chow groups of schemes 226
§7. Homological Chow groups of DM stacks 232
§8. Operational Chow groups of schemes and DM stacks 236
Chapter VI. Algebraic Geometric Introduction to the Gravitational Quan¬
tum Cohomology 245
§1. Virtual fundamental classes 245
§2. Gravitational descendants and Virasoro constraints 250
§3. Correlators and forgetful maps 256
§4. Correlators and boundary maps 266
§5. The simplest Virasoro constraints 270
§6. Generalized correlators 272
§7. Generating functions on the large phase space 278
Bibliography 285
Subject Index 299
|
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| id | DE-604.BV012798013 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:33:50Z |
| institution | BVB |
| isbn | 0821819178 |
| language | English |
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| physical | XIII, 303 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | AMS |
| record_format | marc |
| series | American Mathematical Society: Colloquium publications |
| series2 | American Mathematical Society: Colloquium publications |
| spelling | Manin, Jurij I. 1937-2023 Verfasser (DE-588)121177580 aut Frobenius manifolds, quantum cohomology and moduli spaces Yuri I. Manin Providence, RI AMS 1999 XIII, 303 S. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Colloquium publications 47 Kohomologie (DE-588)4031700-6 gnd rswk-swf Modulraum (DE-588)4183462-8 gnd rswk-swf Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd rswk-swf Symplektische Mannigfaltigkeit (DE-588)4290704-4 s DE-604 Kohomologie (DE-588)4031700-6 s Modulraum (DE-588)4183462-8 s Erscheint auch als Online-Ausgabe 978-1-4704-3193-8 American Mathematical Society: Colloquium publications 47 (DE-604)BV035417609 47 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008703213&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Manin, Jurij I. 1937-2023 Frobenius manifolds, quantum cohomology and moduli spaces American Mathematical Society: Colloquium publications Kohomologie (DE-588)4031700-6 gnd Modulraum (DE-588)4183462-8 gnd Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd |
| subject_GND | (DE-588)4031700-6 (DE-588)4183462-8 (DE-588)4290704-4 |
| title | Frobenius manifolds, quantum cohomology and moduli spaces |
| title_auth | Frobenius manifolds, quantum cohomology and moduli spaces |
| title_exact_search | Frobenius manifolds, quantum cohomology and moduli spaces |
| title_full | Frobenius manifolds, quantum cohomology and moduli spaces Yuri I. Manin |
| title_fullStr | Frobenius manifolds, quantum cohomology and moduli spaces Yuri I. Manin |
| title_full_unstemmed | Frobenius manifolds, quantum cohomology and moduli spaces Yuri I. Manin |
| title_short | Frobenius manifolds, quantum cohomology and moduli spaces |
| title_sort | frobenius manifolds quantum cohomology and moduli spaces |
| topic | Kohomologie (DE-588)4031700-6 gnd Modulraum (DE-588)4183462-8 gnd Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd |
| topic_facet | Kohomologie Modulraum Symplektische Mannigfaltigkeit |
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