Characteristic Classes and the Cohomology of Finite Groups

by C. B. Thomas

Overview

The purpose of this book is to study the relation between the representation ring of a finite group and its integral cohomology by means of characteristic classes. In this way it is possible to extend the known calculations and prove some general results for the integral cohomology ring of a group G of prime power order. Among the groups considered are those of p-rank less than 3, extra-special p-groups, symmetric groups and linear groups over finite fields. An important tool is the Riemann - Roch formula which provides a relation between the characteristic classes of an induced representation, the classes of the underlying representation and those of the permutation representation of the infinite symmetric group. Dr Thomas also discusses the implications of his work for some arithmetic groups which will interest algebraic number theorists. Dr Thomas assumes the reader has taken basic courses in algebraic topology, group theory and homological algebra, but has included an appendix in which he gives a purely topological proof of the Riemann - Roch formula.

Product Details

ISBN-13:	9780521090650
Publisher:	Cambridge University Press
Publication date:	11/27/2008
Series:	Cambridge Studies in Advanced Mathematics , #9
Pages:	144
Product dimensions:	5.90(w) x 8.90(h) x 0.40(d)

Table of Contents

1. Group cohomology; 2. Products and change of group; 3. Relations with subgroups and duality; 4. Spectral sequences; 5. Representations and vector bundles; 6. Bundles over the classifying space for a discrete group; 7. The symmetric group; 8. Finite groups with p-rank less than or equal to 2; 9. Linear groups over finite fields.