Algebra VII

Combinatorial Group Theory Applications to Geometry

AvD.J. Collins,R.I. Grigorchuk

Inbunden, Engelska, 1993

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Beskrivning

This volume of the EMS consists of two parts. The first entitled Combinatorial Group Theory and Fundamental Groups, written by Collins and Zieschang, provides a readable and comprehensive description of that part of group theory which has its roots in topology in the theory of the fundamental group and the theory of discrete groups of transformations. Throughout the emphasis is on the rich interplay between the algebra and the topology and geometry. The second part by Grigorchuk and Kurchanov is a survey of recent work on groups relating to topological manifolds, dealing with equations in groups, particularly in surface groups and free groups, a study in terms of groups of Heegaard decompositions and algorithmic aspects of the Poincare conjecture, as well as the notion of the growth of groups. The authors have included a list of open problems, some of which have not been considered previously. Both parts contain numerous examples, outlines of proofs and full references to the literature. The book will be very useful as a reference and guide to researchers and graduate students in algebra and topology.

Produktinformation

Utgivningsdatum:1993-09-23
Mått:155 x 235 x undefined mm
Format:Inbunden
Språk:Engelska
Serie:Encyclopaedia of Mathematical Sciences
Antal sidor:242
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540547006
Översättare:Cohn, P.M.

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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

Innehållsförteckning

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.

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