The cohomology of the classifying space of $PU(4)$

Abstract

Let $BPU(n)$ be the classifying space of the projective unitary group $PU(n)$. We determine the integral cohomology ring of $BPU(4)$, and the Steenrod algebra structure of its mod $2$ cohomology.

25 pages. An error in Theorem 2.2 was corrected in this version