Characteristic Classes for GO(2n,C)
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The complex Lie group GO(2n,C) by definition consists of all complex matrices A of size 2n, such that A times transpose(A) is a non-zero scalar. In this paper we determine explicitly the singular cohomology ring of the classifying space BGO(2n,C) with mod 2 coefficients, in terms of generators and relations. The method consists of analysing a certain derivation on the cohomology ring of BO(2n) (which is a polynomial ring in the Stiefel-Whitney classes) via a Koszul complex, and using this to `solve' the Gysin sequence for the bundle BO(2n) over BGO(2n,C).
18 pages, LaTeX. This version contains new material, proving correct relationship with odd Chern classes (this was wrongly stated earlier). The version without odd Chern classes will appear in the Asian Journal of Mathematics
18 pages, LaTeX. This version contains new material, proving correct relationship with odd Chern classes (this was wrongly stated earlier). The version without odd Chern classes will appear in the Asian Journal of Mathematics