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*
Donald Yau
*

Cohomology of unitary and sympletic groups

*(Lobachevskii Journal of Mathematics,
Vol.5, pp.57-60)*

We compute the cohomology rings of $U(n)$ and $Sp(n)$ and of their
Stiefel varieties by using the Serre spectral sequence. This approach
is much simpler than the usual method, that of using the cell
structures. The argument here also shows that the cohomology of $U(n)$
is built from those of $U(n - 1)$ and $S^{2n - 1}$ through a fiber
bundle; a similar result holds for $Sp(n)$.}

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