Characteristic Classes and the Cohomology of Finite Groups
By (author) C. B. Thomas
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Characteristic Classes and the Cohomology of Finite Groups by C. B. Thomas
Book DescriptionThe 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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Book DetailsISBN: 9780521090650
(228mm x 152mm x 9mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 27-Nov-2008
Country of Publication: United Kingdom
Books By Author C. B. Thomas
Geometry of Low-Dimensional Manifolds: Volume 1, Gauge Theory and Algebraic Surfaces, Paperback (January 1991)
This volume is based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds.
Geometry of Low-dimensional Manifolds, Paperback (January 1991)
The second of two volumes based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds. This area has been one of intense research recently, with major breakthroughs that have illuminated the way a number of different subjects interact.
Introduction to Differential Topology, Paperback (September 1982)» View all books by C. B. Thomas
This book is intended as an elementary introduction to differential manifolds.
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