Higher homotopy-commutativity

Williams, Frank

doi:10.1090/s0002-9947-1969-0240818-9

Cited by 26 publications

(29 citation statements)

References 12 publications

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“…Later Williams [26] considered another type of higher homotopy commutativity which is weaker than the one of Sugawara. In his combinatorial definition, Williams used polyhedra called the permutohedra which are originally introduced by Milgram [18] to construct approximations to the iterated loop spaces.…”

Section: Introductionmentioning

confidence: 99%

Higher homotopy commutativity of 𝐻-spaces and the permuto-associahedra

Hemmi

Kawamoto

2004

Trans. Amer. Math. Soc.

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Abstract. In this paper, we give a combinatorial definition of a higher homotopy commutativity of the multiplication for an An-space. To give the definition, we use polyhedra called the permuto-associahedra which are constructed by Kapranov. We also show that if a connected Ap-space has the finitely generated mod p cohomology for a prime p and the multiplication of it is homotopy commutative of the p-th order, then it has the mod p homotopy type of a finite product of Eilenberg-Mac Lane spaces K(Z, 1)s, K(Z, 2)s and K(Z/p i , 1)s for i ≥ 1.

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Section: Introductionmentioning

confidence: 99%

Higher homotopy commutativity of 𝐻-spaces and the permuto-associahedra

Hemmi

Kawamoto

2004

Trans. Amer. Math. Soc.

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“…Williams [26] introduced another kind of the higher homotopy commutativity of loop spaces. By a result of McGibbon [19,Prop.…”

Section: Now We Can Prove Theorem B As Followsmentioning

confidence: 99%

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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“…The geometric and simplicial properties of these polygons were examined in [10], [12] and [2]. Here I will give only a rough sketch of the few details I will use.…”

Section: The Permutohedra and Berger ^S Constructionmentioning

confidence: 99%

“…Similar to the associahedra introduced by Stasheff in [II], Williams uses the permutohedra and the Milgramconst ruction in [12] to define his notion of C^-spaces, which is used in several subsequent papers, and is occuring in papers of McGibbon and Hemmi (see for example [9] and [7]). …”

mentioning

confidence: 99%

The Milgram non-operad

Brinkmeier¹

1999

Annales De L’institut Fourier

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Higher homotopy-commutativity

Cited by 26 publications

References 12 publications

Higher homotopy commutativity of 𝐻-spaces and the permuto-associahedra

Higher homotopy commutativity of 𝐻-spaces and the permuto-associahedra

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

The Milgram non-operad

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