Homology exponents for -spaces

  • Alain Clément

    Vevey, Switzerland
  • Jérôme Scherer

    EPFL, Lausanne, Switzerland


We say that a space admits a \emph{homology exponent} if there exists an exponent for the torsion subgroup of . Our main result states that if an -space of finite type admits a homology exponent, then either it is, up to -completion, a product of spaces of the form , , , and , or it has infinitely many non-trivial homotopy groups and -invariants. Relying on recent advances in the theory of -spaces, we then show that simply connected -spaces whose mod cohomology is finitely generated as an algebra over the Steenrod algebra do not have homology exponents, except products of mod finite -spaces with copies of and .

Cite this article

Alain Clément, Jérôme Scherer, Homology exponents for -spaces. Rev. Mat. Iberoam. 24 (2008), no. 3, pp. 963–980

DOI 10.4171/RMI/562