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arXiv · 2501.07797

A counterexample to a conjecture of Adams

Feifei Fan
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Abstract

A conjecture due to J. F. Adams says that, for any odd prime $p$, the mod $p$ cohomology ring of the classifying space of a connected compact Lie group is detected by its elementary abelian $p$-subgroups. In this paper, we show that the mod $3$ cohomology ring of the classifying space of the projective unitary group $PU(9)$ is not detected by its elementary abelian $3$-subgroups, providing a counterexample to this conjecture. We also obtain many algebraic results as byproducts.

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Feifei Fan. 2025-01-14. A counterexample to a conjecture of Adams. https://arxiv.org/abs/2501.07797

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