Higher homotopy commutativity of H-spaces and homotopy localizations

• Autores: Yusuke Kawamoto
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 231, Nº 1, 2007, págs. 103-126
• Idioma: inglés
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• Resumen

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