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Characteristic classes for permutation representations

Published online by Cambridge University Press:  24 October 2008

G. B. Segal  and
C. T. Stretch
G. B. Segal
Affiliation:
University of Oxford
C. T. Stretch
Affiliation:
University of Western Australia
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Extract

To a finite-dimensional real representation V of a finite group G there are associated its Stiefel–Whitney classes wk (V) (k = 1, 2, 3, …) in the cohomology groups Hk(G; ). ( is the field with two elements.) The total Stiefel-Whitney class

in the ring H*(G; is natural with respect to G in the obvious sense, and, in addition,

(a) exponential, i.e. w(V ⊕ W) = w(V).w(W),and

(b) stable, i.e. w(V) = 1 when F is a trivial representation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 2 , September 1981 , pp. 265 - 272
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

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