On the mod p cohomology of BPU(p)

Abstract

We study the mod p cohomology of the classifying space of the projective unitary group PU(p). We first proof that old conjectures due to J.F. Adams, and Kono and Yagita about the structure of the mod p cohomology of classifying space of connected compact Lie groups held in the case of PU(p). Finally, we proof that the classifying space of the projective unitary group PU(p) is determined by its mod p cohomology as an unstable algebra over the Steenrod algebra for p>3, completing previous works for the cases p=2,3.

14 pages

Cited by in corpus (7)

• On the Cohomology of the Classifying Spaces of Projective Unitary Groups
• Some torsion classes in the Chow ring and cohomology of $BPG{L}_n$
• On the Brown-Peterson cohomology of $BP{U}_n$ in lower dimensions and the Thom map
• A distinguished subring of the Chow ring and cohomology of $BPG{L}_n$
• Milnor operations and classifying spaces
• The cohomology of $BPU(p^m)$ and invariant polynomials
• Modular invariants detecting the cohomology of BF_4 at the prime 3