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 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.

1. Combinational group theory; 2. Spaces and their paths; 3. Groupoids; 4. The fundamental groupoid and the fundamental group; 5. Complexes; 6. Coverings of spaces and complexes; 7. Coverings and group theory; 8. Bass-serre theory; 9. Decision problems; 10. Further topics.

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.