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Riemann-Roch formulae for group representations

Published online by Cambridge University Press:  26 February 2010

C. B. Thomas
C. B. Thomas
Affiliation:
Department of Mathematics, University College London.
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Extract

Our investigation starts from the question: is the even dimensional cohomology of the non-abelian group of order p3 and exponent p generated by Chern classes? From the computation of the complete cohomology ring in [8] one quickly sees that the essential problem is to express elements of the form cor (γk), γ ∈ H2 (k, ℤ), K a subgroup of index p, in terms of Chern classes. For a more general pair of groups (K ≤ G) it is known, see [7] that the best for which one can hope is a description of some multiple of cor (γk) in this way. Our first theorem shows that, under suitable hypotheses (satisfied in particular by the example of order p3) the numerical factor may be removed. Thus

Type
Research Article
Information
Mathematika , Volume 20 , Issue 2 , December 1973 , pp. 253 - 262
Copyright
Copyright © University College London 1973

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References

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