Homotopy classification of spaces with interesting cohomology and a conjecture of Cooke part I

Aguadé, Jaume; Broto, Carles; Notbohm, Dietrich

doi:10.1016/0040-9383(94)90023-x

Cited by 22 publications

(31 citation statements)

References 15 publications

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“…, realizing every BSS, which could possibly be associated to this unstable algebra by our set of axioms, are discussed in [2]. Thus we regard (1), (2) and (3) above as a reasonable set of axioms for a BSS associated to an unstable algebra over the Steenrod algebra.…”

Section: Conventions and Terminologymentioning

confidence: 99%

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On The Homotopy Type of 𝐵𝐺 for Certain Finite 2-Groups 𝐺

Broto

Levi

1997

Trans. Amer. Math. Soc.

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Abstract. We consider the homotopy type of classifying spaces BG, where G is a finite p-group, and we study the question whether or not the mod p cohomology of BG, as an algebra over the Steenrod algebra together with the associated Bockstein spectral sequence, determine the homotopy type of BG. This article is devoted to producing some families of finite 2-groups where cohomological information determines the homotopy type of BG.

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Section: Conventions and Terminologymentioning

confidence: 99%

“…Thus we regard (1), (2) and (3) above as a reasonable set of axioms for a BSS associated to an unstable algebra over the Steenrod algebra. Definition 2.3.…”

Section: Conventions and Terminologymentioning

confidence: 99%

On The Homotopy Type of 𝐵𝐺 for Certain Finite 2-Groups 𝐺

Broto

Levi

1997

Trans. Amer. Math. Soc.

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“…By using the H-structure of X, we have a map f : Sp (2) m → X which induces an isomorphism on the mod 3 cohomology. This completes the proof of Proposition 3.1.…”

Section: Proof Of Proposition 31 By Lemma 32 There Exist Maps Fmentioning

confidence: 99%

“…One should note that the three-connected cover of a simply connected compact Lie group is such an H-space. Other examples are Eilenberg-Mac Lane spaces K(Z, 1), K(Z, 2) and K(Z/p i , 1) for i ≥ 1. At present, only a few results are known for such Hspaces (cf.…”

Section: Introductionmentioning

confidence: 99%

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Homotopy commutativity of $H$-spaces with finitely generated cohomology

Kawamoto

Lin

2001

Trans. Amer. Math. Soc.

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Abstract. We show that a simply connected homotopy associative and homotopy commutative mod 3 H-space with finitely generated mod 3 cohomology is homotopy equivalent to a finite product of K(Z, 2), Sp(2), the threeconnected cover Sp(2) 3 and the homotopy fiber Sp(2) 3; 3 i of the map [3 i ] : Sp(2) → K(Z, 3) for i ≥ 1. Our result also shows that a connected Cp-space in the sense of Sugawara with finitely generated mod p cohomology has the homotopy type of a finite product of K(Z, 1), K(Z, 2) and K(Z/p i , 1) for i ≥ 1.

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