Advances in two-dimensional homotopy and combinatorial group theory:
Saved in:
| Other Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2018
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| Series: | London Mathematical Society lecture note series
446 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | x, 179 Seiten Illustrationen, Diagramme |
| ISBN: | 9781316600900 |
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Record in the Search Index
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| adam_text | Titel: Advances in two-dimensional homotopy and combinatorial group theory
Autor: Metzler, Wolfgang
Jahr: 2018
London Mathematical Society Lecture Note Series: 446 Advances in Two-Dimensional Homotopy and Combinatorial Group Theory Edited by WOLFGANGJMETZLER Johann Wolfgang Goethe-Universität Frankfurt, Germany STEPHAN ROSEBROCK Pädagogische Hochschule Karlsruhe, Germany HI Cambridge university press
Contents Editors’ Preface page ix Addresses of Authors xi 1 A Survey of recent Progress on some Problems in 2-dimensional Topology Jens Harlander 1 1.1 Introduction 1 1.2 Basic definitions 2 1.3 Basic questions 7 1.4 The D(2)-problem and the Eilenberg-Ganea conjecture 9 1.5 Dunwoody’s counterexample to relation lifting 11 1.6 Solving the realization problem for some groups 13 1.7 Exotic presentations of the trefoil group 15 1.8 Exotic almost presentations for the Klein bottle group 17 1.9 Appendix: Geometric Realization for Algebraic 2- Complexes with Finite Fundamental Group 19 By F. Rudolf Beyl and Jens Harlander 2 Further Results concerning the Andrews-Curtis-Conjecture and its Generalizations Cynthia Hog-Angeloni and Wolfgang Metzler 27 2.1 Introduction 27 2.2 Projections onto test groups 28 2.3 Fixed subcomplexes 30 2.4 (AC) for spines of 3-manifolds 33 2.5 Considerations on length 34 2.6 On the future of the Andrews-Curtis problem 35
VI Contents 3 Aspects of TQFT and Computational Algebra Holger Kaden and Simon King 36 3.1 Introduction 36 3.2 The Concept of Topological Quantum Field theory (TQFT) 37 3.3 TQFT on 2-complexes 40 3.4 TQFT on s-move 3-cells 52 3.5 A general construction of state sum invariants 58 3.6 Matveev-Piergallini calculus 68 Labelled Oriented Trees and die Whitehead-Conjecture Stephan Rosebrock 72 4.1 Introduction 72 4.2 The finite and the infinite case 73 4.3 Spherical diagrams 74 4.4 Classes of aspherical LOTs 77 4.5 The asphericity of injective LOTs 86 4.6 Two examples 95 4.7 Virtual Knots and LOTs 96 4.8 L 2 -homology and Whitehead’s asphericity conjecture By Jens Harlander 98 2-Complexes and 3-Manifolds Janina Glock, Cynthia Hog-Angeloni and Sergei Matveev 103 5.1 Introduction 103 5.2 Existence and Uniqueness 104 5.3 ¿-Connectivity of Whitehead Graphs 106 5.4 M.H.A. Newman’s Diamond Lemma and a new version of it 114 5.5 Universal Scheme 117 5.6 Kneser-Milnor Theorem 118 5.7 Prime decompositions of knots in F x I 120 The Relation Gap Problem Jens Harlander 128 6.1 Introduction 128 6.2 The Relation Gap problem 129 6.3 Examples 132 6.4 An Infinite Relation Gap 133 6.5 Efficiency 137 6.6 Presentations with Cyclic Relation Modules 142 6.7 Finite Groups 143
Contents vii 7 On the Relation Gap Problem for Free Products Cynthia Hog-Angeloni and Wolfgang Metzler 149 7.1 Introduction 149 7.2 Semisplit presentations, flower relations and integral flower chains 150 7.3 Applications to the Epstein Groups 158 7.4 Ideas for further work 159 7.5 Flower chains and Splitting with respect to field coefficients 161 7.6 Proof of the Theorem on semisplit Q*’-transformations 165 References 167 Index 177 Erratum 180
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| id | DE-604.BV044671966 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:58:54Z |
| institution | BVB |
| isbn | 9781316600900 |
| language | English |
| lccn | 017049965 |
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| physical | x, 179 Seiten Illustrationen, Diagramme |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | Cambridge University Press |
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| series | London Mathematical Society lecture note series |
| series2 | London Mathematical Society lecture note series |
| spelling | Advances in two-dimensional homotopy and combinatorial group theory edited by Wolfgang Metzler (Johann Wolfgang Goethe-Universität Frankfurt, Germany), Stephan Rosebrock (Pädagogische Hochschule Karlsruhe, Germany) Cambridge Cambridge University Press 2018 x, 179 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier London Mathematical Society lecture note series 446 Homotopy theory Combinatorial group theory Low-dimensional topology Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Dimension 2 (DE-588)4321721-7 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 s Dimension 2 (DE-588)4321721-7 s Kombinatorische Gruppentheorie (DE-588)4219556-1 s DE-604 Metzler, Wolfgang 1941- (DE-588)117712612 edt Rosebrock, Stephan (DE-588)1147720959 edt London Mathematical Society lecture note series 446 (DE-604)BV000000130 446 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030069301&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Advances in two-dimensional homotopy and combinatorial group theory London Mathematical Society lecture note series Homotopy theory Combinatorial group theory Low-dimensional topology Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd Homotopietheorie (DE-588)4128142-1 gnd Dimension 2 (DE-588)4321721-7 gnd |
| subject_GND | (DE-588)4219556-1 (DE-588)4128142-1 (DE-588)4321721-7 |
| title | Advances in two-dimensional homotopy and combinatorial group theory |
| title_auth | Advances in two-dimensional homotopy and combinatorial group theory |
| title_exact_search | Advances in two-dimensional homotopy and combinatorial group theory |
| title_full | Advances in two-dimensional homotopy and combinatorial group theory edited by Wolfgang Metzler (Johann Wolfgang Goethe-Universität Frankfurt, Germany), Stephan Rosebrock (Pädagogische Hochschule Karlsruhe, Germany) |
| title_fullStr | Advances in two-dimensional homotopy and combinatorial group theory edited by Wolfgang Metzler (Johann Wolfgang Goethe-Universität Frankfurt, Germany), Stephan Rosebrock (Pädagogische Hochschule Karlsruhe, Germany) |
| title_full_unstemmed | Advances in two-dimensional homotopy and combinatorial group theory edited by Wolfgang Metzler (Johann Wolfgang Goethe-Universität Frankfurt, Germany), Stephan Rosebrock (Pädagogische Hochschule Karlsruhe, Germany) |
| title_short | Advances in two-dimensional homotopy and combinatorial group theory |
| title_sort | advances in two dimensional homotopy and combinatorial group theory |
| topic | Homotopy theory Combinatorial group theory Low-dimensional topology Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd Homotopietheorie (DE-588)4128142-1 gnd Dimension 2 (DE-588)4321721-7 gnd |
| topic_facet | Homotopy theory Combinatorial group theory Low-dimensional topology Kombinatorische Gruppentheorie Homotopietheorie Dimension 2 |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030069301&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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