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Combinatorial group theory : a topological approach /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
1989.
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| Colección: | London Mathematical Society student texts ;
14. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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
- 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
- 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