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

Natàlia Castellana, Juan A. Crespo, Jérôme Scherer

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

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. © Walter de Gruyter 2007.
Original languageEnglish
Pages (from-to)555-561
JournalForum Mathematicum
Volume19
Issue number3
DOIs
Publication statusPublished - 23 May 2007

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