Higher homotopy commutativity of H-spaces and homotopy localizations

Yusuke Kawamoto

Vol. 231 (2007), No. 1, 103–126

DOI: 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 𝒜_p^∗. Our result shows that for any prime p, if X is a connected AC_p-space whose mod p cohomology H^∗(X; ℤ∕p) is finitely generated as an algebra over 𝒜_p^∗, then X has the mod p homotopy type of a Postnikov H-space.

Keywords

higher homotopy commutativity, homotopy localizations, H-spaces, A_n-spaces, AC_n-spaces

Mathematical Subject Classification 2000

Primary: 55P45, 55P48

Secondary: 55P15, 55P65

Milestones

Received: 11 January 2006

Revised: 17 December 2006

Accepted: 19 December 2006

Published: 1 May 2007