A Fractal-Like Algebraic Splitting of the Classifying Space for Vector Bundles

DOI10.2307/2001182zbMath0666.55012OpenAlexW4240938368MaRDI QIDQ3817298

Vincent Giambalvo, Douglas C. Ravenel, David J. Pengelley

Publication date: 1988

Full work available at URL: https://doi.org/10.2307/2001182

zbMATH Keywords

mod 2 Steenrod algebraBrown-Gitler modules\(A_ n\)-splitting of \(B_ n\)algebra grading of \(H_ *BO\)classifying space for real K-theoryn-th distinct connective cover of BOpolynomial generators for \(H_ *BO\)

Mathematics Subject Classification ID

Stable homotopy theory, spectra (55P42) Other types of cobordism (57R90) Homology of classifying spaces and characteristic classes in algebraic topology (55R40) Topological (K)-theory (55N15) Homology and homotopy of (Bmathrm{O}) and (Bmathrm{U}); Bott periodicity (55R45) Hopf algebras (aspects of homology and homotopy of topological groups) (57T05)

Related Items (1)

Sheared algebra maps and operation bialgebras for mod 2 homology and cohomology

Cites Work

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• Connective coverings of BO and immersions of projective spaces
• The homology of MSpin
• Husemoller-Witt decompositions and actions of the Steenrod algebra
• The Nonrealizability of the Quotient A//A 2 of the Steenrod Algebra
• The Splitting of BO〈8〉∧bo and MO〈8〉∧bo
• H ∗ (MO 〈8 〉; Z/2) is an Extended A ∗ 2 -Coalgebra
• Steenrod and Dyer-Lashof Operations on BU
• A Direct Summand in H ∗ (MO 〈8 〉, Z 2 )
• The Immersion Conjecture for RP 8l+7 is False
• On the Stable Decomposition of Ω 2 S r+2
• On the cohomology of 𝑀𝑂⟨8⟩
• An algebraic filtration of H_*(MO;ℤ₂)
• A Stable Decomposition of ω ^N Sⁿ X
• The Structure of the Hopf Algebra H * (BU) over a Z (p) -Algebra
• Determination of H ∗ (BO(k,...,∞), Z 2 ) and H ∗ (BU(k,..., ∞),Z 2 )

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