Surfaces and planar discontinuous groups:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Berlin [u.a.]
Springer
1980
|
| Edition: | Rev. and expanded transl. |
| Series: | Lecture notes in mathematics
835 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 334 S. graph. Darst. |
| ISBN: | 3540100245 0387100245 |
Staff View
MARC
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| 250 | |a Rev. and expanded transl. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1980 | |
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Record in the Search Index
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| adam_text | CONTENTS
Introduction
Interdependence of Topics
1. FREE GROUPS Aid GRAPHS 1
1.1 Free Groups 1
1.2 Word and Conjugacy Problems 3
1.3 Graphs 4
1.4 The Fundamental Group of a Graph 6
1.5 Coverings of Graphs 7
1.6 The Reidemeister Schreier Method for Subgroups 9
1.7 The Nielsen Method 10
1.8 Geometric Interpretation of the Nielsen Property 13
1.9 Automorphisms of a Free Group of Finite Rank 14
Exercises 16
2. 2 DIMENSI0NAL COMPLEXES AND COMBINATORIAL PRESENTATIONS OF GROUPS 19
2.1 Tietze s Theorem 19
2.2 The Reidemeister Schreier Method 24
2.3 Free Products with Amalgamation 31
2.4 2 dimensional Complexes 37
2.5 Coverings 39
2.6 Proof of the Kurosh Theorem 43
2.7 Homology groups 44
2.8 The First Homotopy Group and the Fundamental Group, Seifert
Van Kampen Theorem. Pasting Complexes Together 47
2.9 Grushko s Theorem 48
2.10 On the Nielsen Method in Free Products 51
2.11 On Groups with one Defining Relation 54
2.12 Remarks 59
Exercises 61
3. SURFACES 64
3.1 Definitions 64
3.2 Classification of Finite Surfaces 68
3.3 Kneser s Formula 73
VIII
3.4 Coverings of Surfaces 79
3.5 Types of Simple Closed Curves on Surfaces 84
3.6 Intersection Numbers of Curves 87
3.7 On Continuous Mappings Between Surfaces 94
3.8 Remarks 101
Exercises 102
4. PLANAR DISCONTINUOUS GROUPS 106
4.1 Planar Nets 106
4.2 Automorphisms of a Planar Net 109
4.3 Automorphism Groups of Planar lleto 112
4.4 Fundamental Domains 115
4.5 The Algebraic Structure of Planar Discontinuous Groups 116
4.6 Classification of Planar Discontinuous Groups 120
4.7 Existence Proof 122
4.8 On the Algebraic Structure of Planar Groups 125
4.9 The Word and Conjugacy Problems 128
4.10 Surface Subgroups of Finite Index 132
4.11 On Planar Groups with Non Compact Fundamental Domain 137
4.12 On Decompositions of Discontinuous.Groups of the Plane 140
4.13 Planar Group Presentations and Diagrams 14 2
4.14 Subgroups and the Riemann Hurwitz Formula 150
4.15 Finite Groups Acting on Closed Surfaces 160
4.16 On the Rank of Planar Discontinuous Groups 170
Exercises 174
5. AUTOMORPHISMS OF PLANAR GROUPS 178
5.1 Preliminary Considerations 178
5.2 Binary Products 179
5.3 Homotopic Binary Products 184
5.4 Free Generators of the Group of Relations 190
5.5 The Mapping Matrix 192
5.6 The Dehn Nielsen Theorem I94
5.7 Nielsen s Theorem for Bounded Surfaces 196
5.8 Automorphisms of Planar Groups 199
5.9 Combinatorial Isotopy 204
5.10 A solution of the Word and Conjugacy Problem in Fundamental
Groups of Surfaces 205
5.11 Isotopy of Free Homotopic Simple Closed Curves 206
5.12 Basepoint Preserving Isotopies of Simple Closed Curves 211
IX
5.13 Inner Automorphisms and Isotopies 214
5.14 The Baer Theorem for Planar Discontinuous Groups 216
5.15 On the Mapping Class Group 227
5.16 Coverings and the Mapping Class Group 232
Exercises 239
6. ON THE COMPLEX ANALYTIC THEORY OF RIEMANN SURFACES AND PLANAR
DISCONTINUOUS GROUPS
6.1 Introduction 242
6.2 Structures on Surfaces 242
6.3 The Non Euclidean Plane 244
6.4 Planar Discontinuous Groups 247
6.5 On the Modular Problem 250
6.6 Teichmuller Theory and its Consequences 251
6.7 A Basis for a Teichmuller Theory 255
6.8 The Classical Foundation 263
6.9 Teichmuller Spaces 265
6.10 Some Lemmas from Hyperbolic Geometry 266
6.11 Canonical Polygons 273
6.12 Automorphisms of Finite Order 283
Exercises 285
7. ON THE TOPOLOGICAL THEORY OF SURFACES 287
7.1 Homological Properties of Subsets of the Plane 287
7.2 Local Path Connectivity 291
7.3 Construction of a Crosscut 294
7.4 The Schonflies Theorem 299
7.5 Triangulation and Hauptvermutung for Surfaces 304
Exercises 308
Books on surface theory and related subjects 310
Bibliography 311
List of fetation 330
Index 331
|
| any_adam_object | 1 |
| author | Zieschang, Heiner 1936-2004 Vogt, Elmar Coldewey, Hans-Dieter |
| author_GND | (DE-588)11564489X |
| author_facet | Zieschang, Heiner 1936-2004 Vogt, Elmar Coldewey, Hans-Dieter |
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| author_sort | Zieschang, Heiner 1936-2004 |
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| building | Verbundindex |
| bvnumber | BV002265401 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 |
| ctrlnum | (OCoLC)7073544 (DE-599)BVBBV002265401 |
| dewey-full | 512/.22 510 |
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| dewey-ones | 512 - Algebra 510 - Mathematics |
| dewey-raw | 512/.22 510 |
| dewey-search | 512/.22 510 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Rev. and expanded transl. |
| format | Book |
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| id | DE-604.BV002265401 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:43:02Z |
| institution | BVB |
| isbn | 3540100245 0387100245 |
| language | English German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001488684 |
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| physical | IX, 334 S. graph. Darst. |
| publishDate | 1980 |
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| publishDateSort | 1980 |
| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Zieschang, Heiner 1936-2004 Verfasser (DE-588)11564489X aut Flächen und ebene diskontinuierliche Gruppen Surfaces and planar discontinuous groups Heiner Zieschang ; Elmar Vogt ; Hans-Dieter Coldewey Rev. and expanded transl. Berlin [u.a.] Springer 1980 IX, 334 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 835 Groupes discontinus Groupes discontinus ram Surfaces (Mathématiques) Surfaces (Mathématiques) ram Topologie combinatoire Topologie combinatoire ram Combinatorial topology Discontinuous groups Surfaces Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Fläche (DE-588)4129864-0 gnd rswk-swf Diskrete Gruppe (DE-588)4135541-6 gnd rswk-swf Kombinatorische Topologie (DE-588)4137530-0 gnd rswk-swf Fläche (DE-588)4129864-0 s Gruppentheorie (DE-588)4072157-7 s DE-604 Kombinatorische Topologie (DE-588)4137530-0 s Diskrete Gruppe (DE-588)4135541-6 s Vogt, Elmar Verfasser aut Coldewey, Hans-Dieter Verfasser aut Lecture notes in mathematics 835 (DE-604)BV000676446 835 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001488684&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zieschang, Heiner 1936-2004 Vogt, Elmar Coldewey, Hans-Dieter Surfaces and planar discontinuous groups Lecture notes in mathematics Groupes discontinus Groupes discontinus ram Surfaces (Mathématiques) Surfaces (Mathématiques) ram Topologie combinatoire Topologie combinatoire ram Combinatorial topology Discontinuous groups Surfaces Gruppentheorie (DE-588)4072157-7 gnd Fläche (DE-588)4129864-0 gnd Diskrete Gruppe (DE-588)4135541-6 gnd Kombinatorische Topologie (DE-588)4137530-0 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4129864-0 (DE-588)4135541-6 (DE-588)4137530-0 |
| title | Surfaces and planar discontinuous groups |
| title_alt | Flächen und ebene diskontinuierliche Gruppen |
| title_auth | Surfaces and planar discontinuous groups |
| title_exact_search | Surfaces and planar discontinuous groups |
| title_full | Surfaces and planar discontinuous groups Heiner Zieschang ; Elmar Vogt ; Hans-Dieter Coldewey |
| title_fullStr | Surfaces and planar discontinuous groups Heiner Zieschang ; Elmar Vogt ; Hans-Dieter Coldewey |
| title_full_unstemmed | Surfaces and planar discontinuous groups Heiner Zieschang ; Elmar Vogt ; Hans-Dieter Coldewey |
| title_short | Surfaces and planar discontinuous groups |
| title_sort | surfaces and planar discontinuous groups |
| topic | Groupes discontinus Groupes discontinus ram Surfaces (Mathématiques) Surfaces (Mathématiques) ram Topologie combinatoire Topologie combinatoire ram Combinatorial topology Discontinuous groups Surfaces Gruppentheorie (DE-588)4072157-7 gnd Fläche (DE-588)4129864-0 gnd Diskrete Gruppe (DE-588)4135541-6 gnd Kombinatorische Topologie (DE-588)4137530-0 gnd |
| topic_facet | Groupes discontinus Surfaces (Mathématiques) Topologie combinatoire Combinatorial topology Discontinuous groups Surfaces Gruppentheorie Fläche Diskrete Gruppe Kombinatorische Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001488684&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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