Geometry of Riemann surfaces and Teichmüller spaces:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
North-Holland
1992
|
| Series: | North-Holland Mathematics Studies
169 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 263 Seiten graph. Darst. |
| ISBN: | 0444888462 |
Staff View
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| 245 | 1 | 0 | |a Geometry of Riemann surfaces and Teichmüller spaces |c Mika Seppälä, Academy of Finland, Helsinki, Finland, Tuomas Sorvali, University of Joensuu, Joensuu, Finland |
| 264 | 1 | |a Amsterdam [u.a.] |b North-Holland |c 1992 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Geometry of Mobius transformations 11
1.1 Introduction to Chapter 1 11
1.2 Mobius transformations 12
1.3 Multiplier preserving isomorphisms 17
1.4 Parametrization problem and classes H, V and £ 23
1.5 Geometrical properties of the classes V and H 29
1.6 Parametrization of principal-circle groups by multipliers ... 40
1.7 Orthogonal decompositions and twist parameters 46
2 Quasiconformal mappings 59
2.1 Introduction to Chapter 2 59
2.2 Conformal invariants 59
2.3 Definitions for quasiconformal mappings 61
2.4 Complex dilatation 62
3 Geometry of Riemann surfaces 69
3.1 Introduction to Chapter 3 69
3.2 Riemann and Klein surfaces 69
3.3 Elementary surfaces 71
3.4 Topological classification of surfaces 72
3.5 Discrete groups of Mobius transformations 80
3.6 Uniformization 85
3.7 Models for symmetric surfaces 93
3.8 Hyperbolic metric of Riemann surfaces 95
3.9 Hurwitz Theorem 97
3.10 Horocycles 101
3.11 Nielsen s criterium for discontinuity 104
3.12 Classification of Fuchsian groups 107
3.13 Short closed curves 108
3.14 Collars 109
3.15 Length spectrum 115
7
8 CONTENTS
3.16 Pants decompositions of compact surfaces 117
3.17 Shortest curves on a hyperbolic Riemann surface with a sym¬
metry 120
3.18 Selection of additional simple closed curves on a hyperbolic
Riemann surface with a symmetry 124
3.19 Numerical estimate 129
3.20 Groups of Mobius transformations and matrix groups .... 131
3.21 Traces of commutators 132
3.22 Liftings of Fuchsian groups 135
4 Moduli problems and Teichmiiller spaces 137
4.1 Introduction to Chapter 4 137
4.2 Quasiconformal mappings of Riemann surfaces 141
4.3 Teichmiiller spaces of Klein surfaces 144
4.4 Teichmiiller spaces of Beltrami differentials 147
4.5 Non-classical Klein surfaces 148
4.6 Teichmiiller spaces of genus 1 surfaces 150
4.7 Teichmiiller spaces of reflection groups 152
4.8 Parametrization of Teichmuller spaces 155
4.9 Geodesic length functions 158
4.10 Discontinuity of the action of the modular group 162
4.11 Representations of groups 164
4.12 The algebraic structure 170
4.13 Reduction of parameters 172
4.14 Extension to non-classical surfaces 174
5 Moduli spaces 177
5.1 Introduction to Chapter 5 177
5.2 Moduli spaces of smooth Riemann surfaces 178
5.3 Moduli spaces of genus 1 surfaces 180
5.4 Stable Riemann surfaces 185
5.5 Fenchel-Nielsen coordinates 190
5.6 Topology for the moduli space of stable Riemann surfaces . . 192
5.7 Compactness theorem 194
5.8 Symmetric Riemann surfaces and real algebraic curves .... 195
5.9 Connectedness of the real moduli space 197
5.10 Compactness of the real moduli space 201
5.11 Review on results concerning the analytic structure of moduli
spaces of compact Riemann surfaces 204
CONTENTS 9
A Hyperbolic metric and Mobius groups 209
A.I Length and area elements 209
A.2 Isometries of the hyperbolic metric 211
A.3 Geometry of the hyperbolic metric 211
A.4 Matrix groups 213
A.5 Representation of groups 218
A.6 Complex Mobius transformations 223
A.7 Abelian groups of Mobius transformations 231
A.8 Discrete groups of Mobius transformations 238
B Traces of matrices 245
B.I Trace functions 245
Bibliography 249
Subject Index 258
|
| any_adam_object | 1 |
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| author_role | aut aut |
| author_sort | Seppälä, Mika 1951- |
| author_variant | m s ms t s ts |
| building | Verbundindex |
| bvnumber | BV004703551 |
| classification_rvk | SI 867 SK 750 |
| ctrlnum | (OCoLC)58501349 (DE-599)BVBBV004703551 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004703551 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:16:22Z |
| institution | BVB |
| isbn | 0444888462 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002889477 |
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| physical | 263 Seiten graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | North-Holland |
| record_format | marc |
| series | North-Holland Mathematics Studies |
| series2 | North-Holland Mathematics Studies |
| spelling | Seppälä, Mika 1951- Verfasser (DE-588)1025700511 aut Geometry of Riemann surfaces and Teichmüller spaces Mika Seppälä, Academy of Finland, Helsinki, Finland, Tuomas Sorvali, University of Joensuu, Joensuu, Finland Amsterdam [u.a.] North-Holland 1992 263 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier North-Holland Mathematics Studies 169 Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Teichmüller-Raum (DE-588)4131425-6 gnd rswk-swf Riemannsche Fläche (DE-588)4049991-1 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 s DE-604 Teichmüller-Raum (DE-588)4131425-6 s Riemannsche Fläche (DE-588)4049991-1 s Sorvali, Tuomas 1944- Verfasser (DE-588)172380294 aut North-Holland Mathematics Studies 169 (DE-604)BV000003247 169 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002889477&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Seppälä, Mika 1951- Sorvali, Tuomas 1944- Geometry of Riemann surfaces and Teichmüller spaces North-Holland Mathematics Studies Riemannscher Raum (DE-588)4128295-4 gnd Teichmüller-Raum (DE-588)4131425-6 gnd Riemannsche Fläche (DE-588)4049991-1 gnd |
| subject_GND | (DE-588)4128295-4 (DE-588)4131425-6 (DE-588)4049991-1 |
| title | Geometry of Riemann surfaces and Teichmüller spaces |
| title_auth | Geometry of Riemann surfaces and Teichmüller spaces |
| title_exact_search | Geometry of Riemann surfaces and Teichmüller spaces |
| title_full | Geometry of Riemann surfaces and Teichmüller spaces Mika Seppälä, Academy of Finland, Helsinki, Finland, Tuomas Sorvali, University of Joensuu, Joensuu, Finland |
| title_fullStr | Geometry of Riemann surfaces and Teichmüller spaces Mika Seppälä, Academy of Finland, Helsinki, Finland, Tuomas Sorvali, University of Joensuu, Joensuu, Finland |
| title_full_unstemmed | Geometry of Riemann surfaces and Teichmüller spaces Mika Seppälä, Academy of Finland, Helsinki, Finland, Tuomas Sorvali, University of Joensuu, Joensuu, Finland |
| title_short | Geometry of Riemann surfaces and Teichmüller spaces |
| title_sort | geometry of riemann surfaces and teichmuller spaces |
| topic | Riemannscher Raum (DE-588)4128295-4 gnd Teichmüller-Raum (DE-588)4131425-6 gnd Riemannsche Fläche (DE-588)4049991-1 gnd |
| topic_facet | Riemannscher Raum Teichmüller-Raum Riemannsche Fläche |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002889477&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003247 |
| work_keys_str_mv | AT seppalamika geometryofriemannsurfacesandteichmullerspaces AT sorvalituomas geometryofriemannsurfacesandteichmullerspaces |