Derek F. Holt, Sarah Rees, Claas E. Röver
London Mathematical Society Student Texts, Cambridge University Press
Blurb
Fascinating connections exist between group
theory and automata theory, and a wide variety of them are discussed
in this text. Automata can be used in group theory to encode
complexity, to represent aspects of underlying geometry on a space on
which a group acts, and to provide efficient algorithms for practical
computation. There are also many applications in geometric group
theory. The authors provide background material in each of these
related areas, as well as exploring the connections along a number of
strands that lead to the forefront of current research in geometric
group theory. Examples studied in detail include hyperbolic groups,
Euclidean groups, braid groups, Coxeter groups, Artin groups, and
automata groups such as the Grigorchuk group. This book will be a
convenient reference point for established mathematicians who need to
understand background material for applications, and can serve as a
textbook for research students in (geometric) group theory.
- Can be used as a primary text for new postgraduates.
- Contains detailed
coverage of many of the interesting examples arising in geometric
group theory, including hyperbolic groups, manifold groups, braid
groups, Coxeter groups, and more.
- Includes all the necessary background
material, with sketch proofs or exercises for the more important
results on which the applications to group theory depend.