The monodromy group:
Saved in:
| Format: | Electronic eBook |
|---|---|
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2006
|
| Series: | Monografie matematyczne
N.S., 67 |
| Subjects: | |
| Online Access: | BTU01 TUM01 UBA01 UBM01 UBR01 UBT01 UPA01 Volltext Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 537 - 557 |
| Physical Description: | 1 Online-Ressource (XI, 580 S.) graph. Darst. |
| ISBN: | 3764375353 9783764375355 9783764375362 |
| DOI: | 10.1007/3-7643-7536-1 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface vii
1 Analytic Functions and Morse Theory 1
§1 Theorem about Monodromy 1
§2 Morse Lemma 3
§3 The Morse Theory 7
2 Normal Forms of Functions 13
§1 Tougeron Theorem 13
§2 Deformations 17
§3 Proofs of Theorems 2.3 and 2.4 . . . 23
§4 Classification of Singularities 29
3 Algebraic Topology of Manifolds 35
§1 Homology and Cohomology 35
§2 Index of Intersection 40
§3 Homotopy Theory 55
4 Topology and Monodromy of Functions 57
§1 Topology of a Non singular Level 57
§2 Picard Lefschetz Formula 65
§3 Root Systems and Coxeter Groups 82
§4 Bifurcational Diagrams 88
§5 Resolution and Normalization 102
5 Integrals along Vanishing Cycles 117
§1 Analytic Properties of Integrals 117
§2 Singularities and Branching of Integrals 125
§3 Picard Fuchs Equations 128
§4 Gauss Manin Connection 140
§5 Oscillating Integrals 150
6 Vector Fields and Abelian Integrals 159
§1 Phase Portraits of Vector Fields 159
§2 Method of Abelian Integrals 164
§3 Quadratic Centers and Bautin s Theorem 189
vi Contents
7 Hodge Structures and Period Map 195
§1 Hodge Structure on Algebraic Manifolds 196
§2 Hypercohomologies and Spectral Sequences 203
§3 Mixed Hodge Structures 210
§4 Mixed Hodge Structures and Monodromy 224
§5 Period Mapping in Algebraic Geometry 252
8 Linear Differential Systems 267
§1 Introduction 267
§2 Regular Singularities 270
§3 Irregular Singularities 279
§4 Global Theory of Linear Equations 293
§5 Riemann Hilbert Problem 296
§6 The Bolibruch Example 307
§7 Isomonodromic Deformations 315
§8 Relation with Quantum Field Theory 324
9 Holomorphic Foliations. Local Theory 333
§1 Foliations and Complex Structures 334
§2 Resolution for Vector Fields 339
§3 One Dimensional Analytic Diffeomorphisms 346
§4 The Ecalle Approach 360
§5 Martinet Ramis Moduli 366
§6 Normal Forms for Resonant Saddles 378
§7 Theorems of Briuno and Yoccoz 381
10 Holomorphic Foliations. Global Aspects 393
§1 Algebraic Leaves 393
§2 Monodromy of the Leaf at Infinity 411
§3 Groups of Analytic Diffeomorphisms 418
§4 The Ziglin Theory 435
11 The Galois Theory 441
§1 Picard Vessiot Extensions 441
§2 Topological Galois Theory 471
12 Hypergeometric Functions 491
§1 The Gauss Hypergeometric Equation 491
§2 The Picard Deligne Mostow Theory 515
§3 Multiple Hypergeometric Integrals 527
Bibliography 537
Index 559
|
| adam_txt |
Contents
Preface vii
1 Analytic Functions and Morse Theory 1
§1 Theorem about Monodromy 1
§2 Morse Lemma 3
§3 The Morse Theory 7
2 Normal Forms of Functions 13
§1 Tougeron Theorem 13
§2 Deformations 17
§3 Proofs of Theorems 2.3 and 2.4 . . . 23
§4 Classification of Singularities 29
3 Algebraic Topology of Manifolds 35
§1 Homology and Cohomology 35
§2 Index of Intersection 40
§3 Homotopy Theory 55
4 Topology and Monodromy of Functions 57
§1 Topology of a Non singular Level 57
§2 Picard Lefschetz Formula 65
§3 Root Systems and Coxeter Groups 82
§4 Bifurcational Diagrams 88
§5 Resolution and Normalization 102
5 Integrals along Vanishing Cycles 117
§1 Analytic Properties of Integrals 117
§2 Singularities and Branching of Integrals 125
§3 Picard Fuchs Equations 128
§4 Gauss Manin Connection 140
§5 Oscillating Integrals 150
6 Vector Fields and Abelian Integrals 159
§1 Phase Portraits of Vector Fields 159
§2 Method of Abelian Integrals 164
§3 Quadratic Centers and Bautin's Theorem 189
vi Contents
7 Hodge Structures and Period Map 195
§1 Hodge Structure on Algebraic Manifolds 196
§2 Hypercohomologies and Spectral Sequences 203
§3 Mixed Hodge Structures 210
§4 Mixed Hodge Structures and Monodromy 224
§5 Period Mapping in Algebraic Geometry 252
8 Linear Differential Systems 267
§1 Introduction 267
§2 Regular Singularities 270
§3 Irregular Singularities 279
§4 Global Theory of Linear Equations 293
§5 Riemann Hilbert Problem 296
§6 The Bolibruch Example 307
§7 Isomonodromic Deformations 315
§8 Relation with Quantum Field Theory 324
9 Holomorphic Foliations. Local Theory 333
§1 Foliations and Complex Structures 334
§2 Resolution for Vector Fields 339
§3 One Dimensional Analytic Diffeomorphisms 346
§4 The Ecalle Approach 360
§5 Martinet Ramis Moduli 366
§6 Normal Forms for Resonant Saddles 378
§7 Theorems of Briuno and Yoccoz 381
10 Holomorphic Foliations. Global Aspects 393
§1 Algebraic Leaves 393
§2 Monodromy of the Leaf at Infinity 411
§3 Groups of Analytic Diffeomorphisms 418
§4 The Ziglin Theory 435
11 The Galois Theory 441
§1 Picard Vessiot Extensions 441
§2 Topological Galois Theory 471
12 Hypergeometric Functions 491
§1 The Gauss Hypergeometric Equation 491
§2 The Picard Deligne Mostow Theory 515
§3 Multiple Hypergeometric Integrals 527
Bibliography 537
Index 559 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| doi_str_mv | 10.1007/3-7643-7536-1 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:57:17Z |
| indexdate | 2024-07-09T20:54:38Z |
| institution | BVB |
| isbn | 3764375353 9783764375355 9783764375362 |
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| series2 | Monografie matematyczne |
| spelling | The monodromy group Henryk Żołądek Basel [u.a.] Birkhäuser 2006 1 Online-Ressource (XI, 580 S.) graph. Darst. txt rdacontent c rdamedia cr rdacarrier Monografie matematyczne N.S., 67 Literaturverz. S. 537 - 557 Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Monodromiegruppe (DE-588)4194644-3 gnd rswk-swf Monodromie (DE-588)4277667-3 gnd rswk-swf Monodromie (DE-588)4277667-3 s DE-604 Monodromiegruppe (DE-588)4194644-3 s Algebraische Geometrie (DE-588)4001161-6 s 1\p DE-604 Singularität Mathematik (DE-588)4077459-4 s 2\p DE-604 Żołądek, Henryk 1953- Sonstige (DE-588)131370642 oth Monografie matematyczne N.S., 67 (DE-604)BV000003532 67 https://doi.org/10.1007/3-7643-7536-1 Verlag Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015517361&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | The monodromy group Monografie matematyczne Singularität Mathematik (DE-588)4077459-4 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Monodromiegruppe (DE-588)4194644-3 gnd Monodromie (DE-588)4277667-3 gnd |
| subject_GND | (DE-588)4077459-4 (DE-588)4001161-6 (DE-588)4194644-3 (DE-588)4277667-3 |
| title | The monodromy group |
| title_auth | The monodromy group |
| title_exact_search | The monodromy group |
| title_exact_search_txtP | The monodromy group |
| title_full | The monodromy group Henryk Żołądek |
| title_fullStr | The monodromy group Henryk Żołądek |
| title_full_unstemmed | The monodromy group Henryk Żołądek |
| title_short | The monodromy group |
| title_sort | the monodromy group |
| topic | Singularität Mathematik (DE-588)4077459-4 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Monodromiegruppe (DE-588)4194644-3 gnd Monodromie (DE-588)4277667-3 gnd |
| topic_facet | Singularität Mathematik Algebraische Geometrie Monodromiegruppe Monodromie |
| url | https://doi.org/10.1007/3-7643-7536-1 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015517361&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003532 |
| work_keys_str_mv | AT zoładekhenryk themonodromygroup |