Dieser Band der EMS enthält zwei Beiträge. Der erste gibt eine umfassende Darstellung der Teilgebiete in der Gruppentheorie, die zur Lösung topologischer Fragestellungen entwickelt wurden: die kombinatorische Gruppentheorie und die Theorie der Fundamentalgruppe. Der zweite Beitrag behandelt neuere Resultate der Gruppentheorie, die für die Theorie der topologischen Mannigfaltigkeiten relevant sind. Der Leser erhält einen Überblick über die Forschung in diesem Gebiet. Zusätzlich enthält der Text viele Beispiele, skizzierte Beweise und ungelöste Probleme. Das Buch wendet sich an Forscher und Studenten höherer Semester in der Algebra und Topologie.

This book consists of two parts. The first part provides a comprehensive description of that part of group theory which has its roots in topology. The second more advanced part deals with recent work on groups relating to topological manifolds. It is a valuable guide to research in this field. The text contains numerous examples, sketches of proofs and open problems.

A comprehensive description of the roots of topology - Of great use to researchers in group theory and the topology of surfaces - Contains list of open problems, some of which have not been considered previously

Klappentext

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

Inhalt
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.