Higher homotopy commutativity of H-spaces and homotopy localizations

Yusuke Kawamoto

Type: Article

Publication Date: 2007-05-01

Citations: 5

DOI: https://doi.org/10.2140/pjm.2007.231.103

Abstract

In this paper, we prove that the homotopy localization of an AC n -space is an AC n -space so that the universal map is an AC n -map.This result is used to study the higher homotopy commutativity of H-spaces with finitely generated cohomology over the Steenrod algebra Ꮽ * p .Our result shows that for any prime p, if X is a connected AC p -space whose mod p cohomology H * (X; ‫/ޚ‬ p) is finitely generated as an algebra over Ꮽ * p , then X has the mod p homotopy type of a Postnikov H-space.

Locations

Pacific Journal of Mathematics - View - PDF

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+ PDF Chat	On the homotopy-commutativity of groups and loop spaces	1960	Masahiro SUGAWARA
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+	A cohomological proof of the torus theorem	1985	James P. Lin
+	On homotopy commutative H-spaces	1969	J. R. Hubbuck