| Description |
1 online resource (310 pages) : illustrations |
| Series |
London Mathematical Society student texts ; 14 |
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London Mathematical Society student texts ; 14.
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| Contents |
Cover; Title; Copyright; Introduction; Table of contents; CHAPTER 1. COMBINATORIAL GROUP THEORY; 1.1 Free groups; 1.2 Generators and relators; 1.3 Free products; 1.4 Pushouts and amalgamated free products; 1.5 HNN extensions; CHAPTER 2. SPACES AND THEIR PATHS; 2.1 Some point-set topology; 2.2 Paths and homotopies; CHAPTER 3. GROUPOIDS; 3.1 Groupoids; 3.2 Direct limits; CHAPTER 4. THE FUNDAMENTAL GROUPOID AND THE FUNDAMENTAL GROUP; 4.1 The fundamental groupoid and the fundamental group; 4.2 Van Kampen's theorem; 4.3 Covering spaces; 4.4 The circle and the complex plane |
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4.5 Joins and weak joinsCHAPTER 5. COMPLEXES; 5.1 Graphs; 5.2 Complexes and their fundamental groups; 5.3 Free groups and their automorphisms; 5.4 Coverings of complexes; 5.5 Subdivisions; 5.6 Geometric realisations; CHAPTER 6. COVERINGS OF SPACES AND COMPLEXES; CHAPTER 7. COVERINGS AND GROUP THEORY; CHAPTER 8. BASS-SERRE THEORY; 8.1 Trees and free groups; 8.2 Nielsen's method; 8.3 Graphs of groups; 8.4 The structure theorems; 8.5 Applications of the structure theorems; 8.6 Construction of trees; CHAPTER 9. DECISION PROBLEMS; 9.1 Decision problems in general |
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9.2 Some easy decision problems in groups9.3 The word problem; 9.4 Modular machines and unsolvabie word problems; 9.5 Some other unsolvabie problems; 9.6 Higman's embedding theorem; 9.7 Groups with one relator; CHAPTER 10. FURTHER TOPICS; 10.1 Small cancellation theory; 10.2 Other topics; NOTES AND REFERENCES; BIBLIOGRAPHY; INDEX |
| Summary |
In this book, developed from courses taught at the University of London, the author aims to show the value of using topological methods in combinatorial group theory. The topological material is given in terms of the fundamental groupoid, giving results and proofs that are both stronger and simpler than the traditional ones. Several chapters deal with covering spaces and complexes, an important method, which is then applied to yield the major Schreier and Kurosh subgroup theorems. The author presents a full account of Bass-Serre theory and discusses the word problem, in particular, its unsolvability and the Higman Embedding Theorem. Included for completeness are the relevant results of computability theory |
| Bibliography |
Includes bibliographical references (pages 297-305) and index |
| Notes |
Print version record |
| Subject |
Combinatorial group theory.
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Topology.
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MATHEMATICS -- Group Theory.
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Combinatorial group theory
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Topology
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Mathematik
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Kombinatorische Gruppentheorie
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Topologie
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Topologische Gruppe
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Gruppentheorie
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Groupes, Théorie combinatoire des.
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Topologie.
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| Form |
Electronic book
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| ISBN |
9781107361416 |
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1107361419 |
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9780511565878 |
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0511565879 |
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