Algebra VII: Combinatorial Group Theory Applications to Geometry

by D.J. Collins, A.I. Kostrikin (Editor), P.M. Cohn (Translator), R.I. Grigorchuk, I.R. Shafarevich (Editor)

Overview

From the reviews: "... The book under review consists of two monographs on geometric aspects of group theory ... Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest. ..." Bulletin of the London Mathematical Society, 1996

Product Details

ISBN-13:	9783540637042
Publisher:	Springer Berlin Heidelberg
Publication date:	04/24/1998
Series:	Encyclopaedia of Mathematical Sciences
Edition description:	1st ed. 1993. 2nd printing 1998
Pages:	242
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

I. Combinatorial Group Theory and Fundamental Groups.- 1. Group Presentations and 2-Complexes.- 2. Free Groups and Free Products.- 3. Surfaces and Planar Discontinuous Groups.- 4. Cancellation Diagrams and Equations Over Groups.- 5. 3-Manifolds and Knots.- 6. Cohomological Methods and Ends.- 7. Decision Problems.- II. Some Questions of Group Theory Related to Geometry.- 1. Equations in Groups and Some Related Questions.- 2. Splitting Homomorphisms and Some Problems in Topology.- 3. On the Rate of Growth of Groups and Amenable Groups.- Author Index.

Editorial Reviews

From the reviews: "... The book under review consists of two monographs on geometric aspects of group theory ... Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest. ..." Bulletin of the London Mathematical Society, 1996

From the Publisher