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Licensed Unlicensed Requires Authentication Published by De Gruyter June 14, 2007

Relating Postnikov pieces with the Krull filtration: a spin-off of Serre's theorem

  • Natàlia Castellana EMAIL logo , Juan A Crespo and Jérôme Scherer
From the journal


We characterize H-spaces which are p-torsion Postnikov pieces of finite type by a cohomological property together with a necessary acyclicity condition. When the mod p cohomology of an H-space is finitely generated as an algebra over the Steenrod algebra we prove that its homotopy groups behave like those of a finite complex. In particular, a p-complete infinite loop space has a finite number of non-trivial homotopy groups if and only if its mod p cohomology satisfies this finiteness condition.

(Communicated by Frederick R. Cohen)

Received: 2005-06-15
Published Online: 2007-06-14
Published in Print: 2007-05-23

© Walter de Gruyter

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