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

Hemmi, Yutaka; Kawamoto, Yusuke

doi:10.1090/S0002-9947-04-03647-5

Higher homotopy commutativity of -spaces and the permuto-associahedra

Authors: Yutaka Hemmi and Yusuke Kawamoto
Journal: Trans. Amer. Math. Soc. 356 (2004), 3823-3839
MSC (2000): Primary 55P45, 55P48; Secondary 55P15, 52B11
DOI: https://doi.org/10.1090/S0002-9947-04-03647-5
Published electronically: May 11, 2004
MathSciNet review: 2058507
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Abstract: In this paper, we give a combinatorial definition of a higher homotopy commutativity of the multiplication for 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 -space has the finitely generated mod cohomology for a prime and the multiplication of it is homotopy commutative of the -th order, then it has the mod homotopy type of a finite product of Eilenberg-Mac Lane spaces $K(\mathbb{Z},1)$ s, $K(\mathbb{Z},2)$ s and $K(\mathbb{Z}/p^i,1)$ s for $i\ge 1$ .

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