Some Generalized Brown-Gitler Spectra

DOI10.2307/2000121zbMath0597.55006OpenAlexW4212936789MaRDI QIDQ3730649

Mark E. Mahowald, Paul G. Goerss, John D. S. Jones

Publication date: 1986

Full work available at URL: https://doi.org/10.2307/2000121

zbMATH Keywords

generalized cohomologyEilenberg-MacLane spectrumcohomology operationsPostnikov towerp-adic integersmod p Steenrod algebrak-invariantsBrown-Gitler spectracohomology with coefficientsbo\({\mathbb{Z}}/p\)\(BP<1>\)\(bu_{(p)}\)collapsing results for spectral sequencesconnective 2-local KO-theoryMahowald's splitting theoremp-local connective K-theoryresolutions of modules over the Steenrod algebra

Mathematics Subject Classification ID

Stable homotopy theory, spectra (55P42) Generalized (extraordinary) homology and cohomology theories in algebraic topology (55N20) Steenrod algebra (55S10) Generalized cohomology and spectral sequences in algebraic topology (55T25) (K)-theory operations and generalized cohomology operations in algebraic topology (55S25)

Related Items (10)

Enumerating partitions arising in homotopy theory ⋮ Brown-Gitler spectra at \(BP<2>\) ⋮ \(\mathcal {E}_\infty \) ring spectra and elements of Hopf invariant 1 ⋮ On the spectrum \(bo \wedge \)tmf ⋮ The bu cohomology of \(BP<n>\) ⋮ The connective real \(K\)-theory of Brown-Gitler spectra ⋮ The 2-primary Hurewicz image of \(\operatorname{tmf}\) ⋮ Detecting exotic spheres in low dimensions using coker J ⋮ A class of 2-local finite spectra which admit a \(v_2^1\)-self-map ⋮ A generalization of the lambda algebra

Cites Work

• Unnamed Item
• bo-resolutions
• The mod-\(p\) lower central series and the Adams spectral sequence
• A spectrum whose cohomology is a certain cyclic module over the Steenrod algebra
• Odd primary infinite families in stable homotopy theory
• Operations in connective 𝐾-theory
• Pontrjagin Duality for Generalized Homology and Cohomology Theories
• On the Stable Decomposition of Ω 2 S r+2
• GENERALIZED HOMOLOGY AND THE GENERALIZED VECTOR FIELD PROBLEM

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