On the mod 𝑝 cohomology of 𝐵𝑃𝑈(𝑝)

Vavpetič, Aleš; Viruel, Antonio

doi:10.1090/S0002-9947-05-03983-8

On the mod $p$ cohomology of $BPU(p)$
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by Aleš Vavpetič and Antonio Viruel

Trans. Amer. Math. Soc. 357 (2005), 4517-4532

DOI: https://doi.org/10.1090/S0002-9947-05-03983-8

Published electronically: June 10, 2005

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Abstract:

We study the mod $p$ cohomology of the classifying space of the projective unitary group $PU(p)$. We first prove that conjectures due to J.F. Adams and Kono and Yagita (1993) about the structure of the mod $p$ cohomology of the classifying space of connected compact Lie groups hold in the case of $PU(p)$. Finally, we prove 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 work by Dwyer, Miller and Wilkerson (1992) and Broto and Viruel (1998) for the cases $p=2,3$.

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