Verfügbarkeit: Surfaces and planar discontinuous groups

Surfaces and planar discontinuous groups:

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Bibliographische Detailangaben
Beteiligte Personen:	Zieschang, Heiner 1936-2004 (VerfasserIn), Vogt, Elmar (VerfasserIn), Coldewey, Hans-Dieter (VerfasserIn)
Format:	Buch
Sprache:	Englisch Deutsch
Veröffentlicht:	Berlin [u.a.] Springer 1980
Ausgabe:	Rev. and expanded transl.
Schriftenreihe:	Lecture notes in mathematics 835
Schlagwörter:	Groupes discontinus Surfaces (Mathématiques) Topologie combinatoire Combinatorial topology Discontinuous groups Surfaces Gruppentheorie Fläche Diskrete Gruppe Kombinatorische Topologie
Links:	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
Umfang:	IX, 334 S. graph. Darst.
ISBN:	3540100245 0387100245

Internformat

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Datensatz im Suchindex

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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
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author	Zieschang, Heiner 1936-2004 Vogt, Elmar Coldewey, Hans-Dieter
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indexdate	2024-12-20T07:48:34Z
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language	English German
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physical	IX, 334 S. graph. Darst.
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series	Lecture notes in mathematics
series2	Lecture notes in mathematics
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
volume_link	(DE-604)BV000676446
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