Homological Group Theory: (Series Number 36 London Mathematical Society Lecture Note Series)

In 1977 several eminent mathematicians were invited to Durham to present papers at a short conference on homological and combinatorial techniques in group theory. The lectures, published here, aimed at presenting in a unified way new developments in the area. Group theory is approached from a geometrical viewpoint and much of the material has not previously been published. The various ways in which topological ideas can be used in group theory are also brought together. The volume concludes with an extensive set of problems, ranging from explicit questions demanding detailed calculation to fundamental questions motivating research in the area. These lectures will be of interest mainly to researchers in pure mathematics but will also prove useful in connection with relevant postgraduate courses.

Table of Contents:
Preface; Introduction; 1. Traces and Euler characteristics Hyman Bass; 2. Groups of virtually finite dimension Kenneth S. Brown; 3. Free abelianised extensions of finite groups K. W. Gruenberg; 4. Arithmetic groups J.-P. Serre; 5. Topological methods in group theory Peter Scott and Terry Wall; 6. An example of a finite presented solvable group Herbert Abels; 7. SL3 (Fq[t]) is not finitely presentable Helmut Behr; 8. Two-dimensional Poincaré duality groups and pairs Robert Bieri and Beno Eckmann; 9. Metabelian quotients of finitely presented soluble groups are finitely presented Robert Bieri and Ralph Strebel; 10. Soluble groups with coherent group rings Robert Bieri and Ralph Strebel; 11. Cohomological aspects of 2-graphs, II Peter J. Cameron; 12. Recognizing free factors M. J. Dunwoody; 13. Trees of homotopy of (n, m)-complexes Michael Dyer; 14. Geometric structure of surface mapping class groups W. J. Harvey; 15. Cohomology theory of aspherical groups and of small cancellation groups Johannes Huebschmann; 16. Finite groups of deficiency zero D. L. Johnson and E. F. Robertson; 17. Äquivalenzklassen von Gruppenbeschreibungen, Identitäten und einfacher Homotopietyp in niederen Dimensionen Wolfgang Metzler; 19. Applications of Nielsen's reduction method to the solution of combinatorial problems in group theory: a survey Gerhard Rosenberger; 20. Chevalley groups over polynomial rings Christophe Soulé; List of problems edited by Terry Wall.