Two-dimensional homotopy and combinatorial group theory:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Cambridge u.a.
Cambridge Univ. Press
1993
|
| Edition: | 1. publ. |
| Series: | London Mathematical Society: London Mathematical Society lecture note series
197 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 412 S. Ill., graph. Darst. |
| ISBN: | 0521447003 |
Staff View
MARC
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| 245 | 1 | 0 | |a Two-dimensional homotopy and combinatorial group theory |c ed. by Cynthia Hog-Angeloni ... |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge u.a. |b Cambridge Univ. Press |c 1993 | |
| 300 | |a XI, 412 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a London Mathematical Society: London Mathematical Society lecture note series |v 197 | |
| 650 | 7 | |a Groupes combinatoires, théorie des |2 ram | |
| 650 | 7 | |a Homotopie |2 gtt | |
| 650 | 7 | |a Homotopie |2 ram | |
| 650 | 7 | |a Topologie de basse dimension |2 ram | |
| 650 | 4 | |a Combinatorial group theory | |
| 650 | 4 | |a Homotopy theory | |
| 650 | 4 | |a Low-dimensional topology | |
| 650 | 0 | 7 | |a Kombinatorische Gruppentheorie |0 (DE-588)4219556-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Homotopiemannigfaltigkeit |0 (DE-588)4160627-9 |2 gnd |9 rswk-swf |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Hog-Angeloni, Cynthia |e Sonstige |0 (DE-588)1157292216 |4 oth | |
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Record in the Search Index
| _version_ | 1804123867312029696 |
|---|---|
| adam_text | Contents
Editors Preface v
Addresses of Authors vii
I Geometric Aspects of Two Dimensional Complexes 1
Cynthia Hog Angeloni and Wolfgang Metzler
1 Complexes of Low Dimensions and Group Presentations ... 1
2 Simple Homotopy and Low Dimensions 11
3 P.L. Embeddings of 2 Complexes into Manifolds 29
4 Three Conjectures and Further Problems 44
II Algebraic Topology for Two Dimensional Complexes 51
Allan J. Sieradski
1 Techniques in Homotopy 51
2 Homotopy Groups for 2 Complexes 62
3 Equivariant World for 2 Complexes 75
4 Mac Lane Whitehead Algebraic Types 88
III Homotopy and Homology Classification of 2 Complexes 97
M. Paul Latiolais
1 Bias Invariant c Homology Classification 97
2 Classifications for Finite Abelian tti Ill
3 Classifications for Non Finite K (with Cynthia Hog Angeloni) 117
v
vi CONTENTS
IV Crossed Modules and n2 Homotopy Modules 125
Micheal N. Dyer
1 Introduction 125
2 Crossed and Precrossed Modules 126
3 On the Second Homotopy Module of a 2 Complex 140
4 Identity Properties 148
V Calculating Generators of II2 157
William A. Bogley and Steve J. Pride
1 The Theory of Pictures 157
2 Generation of n2 167
3 Applications and Results 176
VI Applications of Diagrams to Decision Problems 189
Giinther Huck and Stephan Rosebrock
1 Introduction 189
2 Decidability and Dehn s Algorithm 190
3 Cayley Graph and van Kampen Diagrams 192
4 Word Hyperbolic Groups and Combings 197
5 Curvature Tests 203
VII Fox Ideals, M Torsion and Applications to Groups and
3 Manifolds 219
Martin Lustig
1 Fox ideals 220
2 Applications of Fox ideals: Tests for the rank, the deficiency
and the homological dimension of a group 225
3 Af torsion: Basic theory 230
CONTENTS vii
4 A/^G), Nielsen equivalence of generating systems and Hee
gaard splittings 233
5 A^ torsion as generalization of the bias and (simple) homotopy
of (G, m) complexes 245
VIII (Singular) 3 Manifolds 251
Cynthia Hog Angeloni and Allan J. Sieradski
1 3 Manifolds 251
2 Singular 3 Manifolds 274
IX Cancellation Results for 2 Complexes and 4 Manifolds
and Some Applications 281
Ian Hambleton and Matthias Kreck
1 A Cancellation Theorem for 2 Complexes 281
2 Stable Classification of 4 Manifolds 286
3 A Cancellation Theorem for Topological 4 Manifolds 290
4 A Homotopy Non Cancellation Theorem for Smooth
4 Manifolds 296
5 A Non Cancellation Example for Simple Homotopy Equivalent
Topological 4 Manifolds 299
6 Application of Cancellation to Exotic Structures on
4 Manifolds 302
7 Topological Embeddings of 2 Spheres into 1 Connected
4 Manifolds and Pseudo free Group Actions 305
X J. H. C. Whitehead s Asphericity Question 309
William A. Bogley
1 Introduction 309
2 The Context of Whitehead s Question 310
3 Structural Results 312
4 Reductions, Evidence and Test Cases 314
viii CONTENTS
5 On the TTj Kernel 320
6 Acyclic Coverings 322
7 Finitely Generated Perfect Subgroups 326
8 Kaplansky s Theorem 328
9 Framed Links 330
10 Open Questions (with J. Howie) 333
XI Zeeman s Collapsing Conjecture 335
Sergei Matveev and Dale Rolfsen
1 Introduction 335
2 Collapsing 338
3 Some Special Ways of Collapsing P2 x I 339
4 1 Collapsibility Modulo 2 Expansions 348
5 Zeeman Conjecture for Special Polyhedra 349
6 Generalizing (Z) to Higher Dimensions 361
7 Open Problems 363
XII The Andrews Curtis Conjecture and its Generalizations 365
Cynthia Hog Angeloni and Wolfgang Metzler
1 Introduction 365
2 Strategies and Characterizations 366
3 (^ Transformations and Presentations of Free Products . . . 373
4 Some Further Results 380
Bibliography 381
Index 408
|
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| dewey-ones | 514 - Topology |
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| discipline | Mathematik |
| edition | 1. publ. |
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| id | DE-604.BV009530554 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:36:35Z |
| institution | BVB |
| isbn | 0521447003 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006292881 |
| oclc_num | 29633587 |
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| physical | XI, 412 S. Ill., graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | London Mathematical Society: London Mathematical Society lecture note series |
| series2 | London Mathematical Society: London Mathematical Society lecture note series |
| spelling | Two-dimensional homotopy and combinatorial group theory ed. by Cynthia Hog-Angeloni ... 1. publ. Cambridge u.a. Cambridge Univ. Press 1993 XI, 412 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: London Mathematical Society lecture note series 197 Groupes combinatoires, théorie des ram Homotopie gtt Homotopie ram Topologie de basse dimension ram Combinatorial group theory Homotopy theory Low-dimensional topology Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd rswk-swf Homotopiemannigfaltigkeit (DE-588)4160627-9 gnd rswk-swf Kombinatorische Gruppentheorie (DE-588)4219556-1 s Homotopiemannigfaltigkeit (DE-588)4160627-9 s DE-604 Hog-Angeloni, Cynthia Sonstige (DE-588)1157292216 oth London Mathematical Society: London Mathematical Society lecture note series 197 (DE-604)BV000000130 197 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006292881&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Two-dimensional homotopy and combinatorial group theory London Mathematical Society: London Mathematical Society lecture note series Groupes combinatoires, théorie des ram Homotopie gtt Homotopie ram Topologie de basse dimension ram Combinatorial group theory Homotopy theory Low-dimensional topology Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd Homotopiemannigfaltigkeit (DE-588)4160627-9 gnd |
| subject_GND | (DE-588)4219556-1 (DE-588)4160627-9 |
| title | Two-dimensional homotopy and combinatorial group theory |
| title_auth | Two-dimensional homotopy and combinatorial group theory |
| title_exact_search | Two-dimensional homotopy and combinatorial group theory |
| title_full | Two-dimensional homotopy and combinatorial group theory ed. by Cynthia Hog-Angeloni ... |
| title_fullStr | Two-dimensional homotopy and combinatorial group theory ed. by Cynthia Hog-Angeloni ... |
| title_full_unstemmed | Two-dimensional homotopy and combinatorial group theory ed. by Cynthia Hog-Angeloni ... |
| title_short | Two-dimensional homotopy and combinatorial group theory |
| title_sort | two dimensional homotopy and combinatorial group theory |
| topic | Groupes combinatoires, théorie des ram Homotopie gtt Homotopie ram Topologie de basse dimension ram Combinatorial group theory Homotopy theory Low-dimensional topology Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd Homotopiemannigfaltigkeit (DE-588)4160627-9 gnd |
| topic_facet | Groupes combinatoires, théorie des Homotopie Topologie de basse dimension Combinatorial group theory Homotopy theory Low-dimensional topology Kombinatorische Gruppentheorie Homotopiemannigfaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006292881&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000130 |
| work_keys_str_mv | AT hogangelonicynthia twodimensionalhomotopyandcombinatorialgrouptheory |