Higher homotopy commutativity of $H$-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 | References | Similar Articles | Additional Information
Abstract: In this paper, we give a combinatorial definition of a higher homotopy commutativity of the multiplication for an $A_n$-space. To give the definition, we use polyhedra called the permuto-associahedra which are constructed by Kapranov. We also show that if a connected $A_p$-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 $K(\mathbb {Z},1)$s, $K(\mathbb {Z},2)$s and $K(\mathbb {Z}/p^i,1)$s for $i\ge 1$.
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Additional Information
Yutaka Hemmi
Affiliation:
Department of Mathematics, Faculty of Science, Kochi University, Kochi 780-8520, Japan
Email:
hemmi@math.kochi-u.ac.jp
Yusuke Kawamoto
Affiliation:
Department of Mathematics, National Defense Academy, Yokosuka 239-8686, Japan
Email:
yusuke@nda.ac.jp
Keywords:
Higher homotopy commutativity,
$H$-spaces,
$A_n$-spaces,
$AC_n$-spaces,
permuto-associahedra
Received by editor(s):
November 27, 2001
Published electronically:
May 11, 2004
Dedicated:
Dedicated to the memory of Professor Masahiro Sugawara
Article copyright:
© Copyright 2004
American Mathematical Society
