The Brown-Peterson cohomology of the classifying spaces of the projective unitary groups 𝑃𝑈(𝑝) and exceptional Lie groups

DOI10.1090/S0002-9947-07-04425-XzbMath1136.55002OpenAlexW1994193089WikidataQ115289073 ScholiaQ115289073MaRDI QIDQ5442130

Nobuaki Yagita, Masaki Kameko

Publication date: 15 February 2008

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-07-04425-x

zbMATH Keywords

classifying spacesAdams spectral sequenceBrown-Peterson theoryDickson invariantMilnor operations

Mathematics Subject Classification ID

Classifying spaces of groups and (H)-spaces in algebraic topology (55R35) Loop spaces (55P35) Bordism and cobordism theories and formal group laws in algebraic topology (55N22) Homology of classifying spaces and characteristic classes in algebraic topology (55R40) Adams spectral sequences (55T15) Homology with local coefficients, equivariant cohomology (55N25) Hopf algebras (aspects of homology and homotopy of topological groups) (57T05) Homology and cohomology of (H)-spaces (57T25)

Related Items (11)

On the Chow rings of classifying spaces for classical groups ⋮ The 𝑝-primary subgroups of the cohomology of 𝐵𝑃𝑈_{𝑛} in dimensions less than 2𝑝+5 ⋮ The \(p\)-primary subgroup of the cohomology of \(BPU_n\) in dimension \(2p + 6\) ⋮ Coniveau filtrations and Milnor operation ⋮ The Chow ring of the classifying space \(\mathrm{BSO}(2n,\mathbb C)\) ⋮ On the integral Tate conjecture over finite fields ⋮ Chow rings of nonabelian \(p\)-groups of order \(p^{3}\) ⋮ On the cohomology of the classifying spaces of projective unitary groups ⋮ The image of the map from group cohomology to Galois cohomology ⋮ Chern subrings ⋮ Some torsion classes in the Chow ring and cohomology of BPGLn

Cites Work

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• The varieties of the mod p cohomology rings of extra special p-groups for an odd prime p
• Cohomology mod 3 of the classifying space of the Lie group $E_6$
• On the Chow ring of the classifying stack of PGL3,ℂ
• Applications of Atiyah–Hirzebruch spectral sequences for motivic cobordism
• Mui invariants and Milnor operations
• On the mod 𝑝 cohomology of 𝐵𝑃𝑈(𝑝)

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