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Cambridge Studies in Advanced Mathematics #9: Characteristic Classes and the Cohomology of Finite Groups

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Cambridge Studies in Advanced Mathematics #9: Characteristic Classes and the Cohomology of Finite Groups Cover

 

Synopses & Reviews

Publisher Comments:

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.

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.

Product Details

ISBN:
9780521090650
Author:
Thomas, C. B.
Publisher:
Cambridge University Press
Location:
Cambridge
Subject:
Group Theory
Subject:
Algebra - General
Subject:
Topology - General
Subject:
Mathematics-Group Theory
Subject:
Topology
Edition Description:
Trade paper
Series:
Cambridge Studies in Advanced Mathematics
Series Volume:
9
Publication Date:
20081131
Binding:
TRADE PAPER
Language:
English
Pages:
144
Dimensions:
5.98x9.01x.33 in. .48 lbs.

Related Subjects

Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » Group Theory
Science and Mathematics » Mathematics » Topology

Cambridge Studies in Advanced Mathematics #9: Characteristic Classes and the Cohomology of Finite Groups New Trade Paper
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Product details 144 pages Cambridge University Press - English 9780521090650 Reviews:
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