Homological Group Theory

C. T. C. Wall

• Publisher: Cambridge University Press
• Year: 1979
• Print ISBN:
  9780521227292
• eBook ISBN:
  9781107107526
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

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

• Cover
• Series Page
• Title
• Copyright
• Contents
• Preface
• Introduction
• 1· Traces and Euler characteristics
• 2· Groups of virtually finite dimension
• 3 · Free abelianised extensions of finite groups
• 4· Arithmetic groups
• 5· Topological methods in group theory
• 6· An example of a finitely presented solvable group
• 7· SL3 ( Fq [t]) is not finitely presentable
• 8· Two-dimensional Poincaré duality groups and pairs
• 9· Metabelian quotients of finitely presented soluble groups are finitely presented
• 10· Soluble groups with coherent group rings
• 11· Cohomological aspects of 2-graphs. II
• 12· Recognizing free factors
• 13· Trees of homotopy types of (π, m)-complexes
• 14· Geometric structure of surface mapping class groups
• 15· Cohomology theory of aspherical groups and of small cancellation groups
• 16· Finite groups of deficiency zero
• 17· Äquivalenzklassen von Gruppenbeschreibungen, ldentitäten und einfacher Homotopietyp in niederen Dimensionen
• 18· Two-dimensional complexes with torsion values not realizable by self-equivalences
• 19 · Applications of Nielsen's reduction method to the solution of combinatorial problems in group theory: a survey
• 20 · Chevalley groups over polynomial rings
• List of problems