ENGLISH

Characteristic classes and cohomology of finite groups

By C. B. Thomas

Book information

Publisher
Cambridge University Press
Year
2008
ISBN
9780521090650, 0521090652
Language
english
Format
DJVU
Filesize
1 MB (1251854 bytes)
Series
Cambridge Studies in Advanced Mathematics 9
Edition
1
Pages
75\75
Topic
Mathematics Algebra
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11

Description

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.

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