Homology exponents for H-spaces

Alain Clément, Jérôme Scherer

Research output: Contribution to journalArticleResearchpeer-review


We say that a space X admits a homology exponent if there exists an exponent for the torsion subgroup of H* (X; ℤ). Our main result states that if an H-space of finite type admits a homology exponent, then either it is, up to 2-completion, a product of spaces of the form Bℤ/2 r, S1, CP∞, and K(ℤ, 3), or it has infinitely many non-trivial homotopy groups and k-invariants. Relying on recent advances in the theory of H-spaces, we then show that simply connected H-spaces whose mod 2 cohomology is finitely generated as an algebra over the Steenrod algebra do not have homology exponents, except products of mod 2 finite H-spaces with copies of CP∞ and K(ℤ, 3).
Original languageEnglish
Pages (from-to)963-980
JournalRevista Matematica Iberoamericana
Issue number3
Publication statusPublished - 1 Jan 2008


  • H-space
  • Homology exponent
  • Loop space
  • Steenrod algebra


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