The $p$-primary subgroups of the cohomology of $BP{U}_n$ in dimensions less than $2p+5$

Abstract

Let $P{U}_n$ the projective unitary group of rank $n$ and $BP{U}_n$ its classifying space. For an odd prime $p$, we extend previous results to a compete description of $H^s(BP{U}_n;\mathbb{Z}{)}_{(p)}$ for $s<2p+5$ by showing that the $p$-primary subgroups of $H^s(BP{U}_n;\mathbb{Z})$ are trivial for $s=2p+3$ and $s=2p+4$.

13 pages. Minor Changes.To appear in the Proceedings of the AMS