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The BrownPeterson cohomology of the classifying spaces of the projective unitary groups PU(p) and exceptional Lie group Trans
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"... Abstract. For a fixed prime p, we compute the BrownPeterson cohomologies of classifying spaces of PU(p) and exceptional Lie groups by using the Adams spectral sequence. In particular, we see that BP ∗ (BPU(p)) and K(n) ∗ (BPU(p)) are even dimensionally generated. 1. ..."
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Abstract. For a fixed prime p, we compute the BrownPeterson cohomologies of classifying spaces of PU(p) and exceptional Lie groups by using the Adams spectral sequence. In particular, we see that BP ∗ (BPU(p)) and K(n) ∗ (BPU(p)) are even dimensionally generated. 1.
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"... arXiv version: fonts, pagination and layout may vary from GTM published version Modular invariants detecting the cohomology of BF4 at the prime 3 CARLES BROTO Attributed to J F Adams is the conjecture that, at odd primes, the mod–p cohomology ring of the classifying space of a connected compact Lie ..."
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arXiv version: fonts, pagination and layout may vary from GTM published version Modular invariants detecting the cohomology of BF4 at the prime 3 CARLES BROTO Attributed to J F Adams is the conjecture that, at odd primes, 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 note we rely on Toda’s calculation of H ∗ (BF4; F3) in order to show that the conjecture holds in case of the exceptional Lie group F4. To this aim we use invariant theory in order to identify parts of H ∗ (BF4; F3) with invariant subrings in the cohomology of elementary abelian 3–subgroups of F4. These subgroups themselves are identified via the Steenrod algebra action on H ∗ (BF4; F3). 55R40; 55S10, 13A50 1