Combinatorial Group Theory: A Topological Approach

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CUP Archive, Aug 17, 1989 - Mathematics - 310 pages
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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.
 

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Contents

COMBINATORIAL GROUP THEORY
1
SPACES AND THEIR PATHS
49
GROUPOIDS
62
THE FUNDAMENTAL GROUPOID AND THE FUNDAMENTAL
74
COMPLEXES
113
COVERINGS OF SPACES AND COMPLEXES
151
BASSSERRE THEORY
182
DECISION PROBLEMS
243
FURTHER TOPICS
286
BIBLIOGRAPHY
297
INDEX
306
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