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The BrownPeterson cohomology of the classifying spaces of the projective unitary groups PU(p) and exceptional Lie group Trans
 of A.M.S
"... 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.
Coniveau filtration of cohomology of groups
 Department of Mathematics, Faculty of Science, Ryukyu University
"... Abstract. We consider natural ltrations of H(BG;Z=p) for a compact Lie group G, such that (Fi) Fi−1 for the Bockstein operation. An example of such ltrations is dened by i = 2n − m for elements in the image from the motivic cohomology Hm;n(BG;Z=p). For some cases e.g., On, PGLp, we see that this l ..."
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Cited by 1 (1 self)
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Abstract. We consider natural ltrations of H(BG;Z=p) for a compact Lie group G, such that (Fi) Fi−1 for the Bockstein operation. An example of such ltrations is dened by i = 2n − m for elements in the image from the motivic cohomology Hm;n(BG;Z=p). For some cases e.g., On, PGLp, we see that this ltration coincides the coniveau ltration dened by Grothendieck, 1.
Modular invariants detecting the cohomology of BF4 at the prime 3
, 2007
"... 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 hol ..."
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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).