JournalsrmiVol. 24, No. 3pp. 963–980

Homology exponents for HH-spaces

  • Alain Clément

    Vevey, Switzerland
  • Jérôme Scherer

    EPFL, Lausanne, Switzerland
Homology exponents for $H$-spaces cover
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We say that a space XX admits a \emph{homology exponent} if there exists an exponent for the torsion subgroup of H(X;Z)H^*(X;\mathbb Z). Our main result states that if an HH-space of finite type admits a homology exponent, then either it is, up to 22-completion, a product of spaces of the form BZ/2rB\mathbb Z/2^r, S1S^1, CP\mathbb C P^\infty, and K(Z,3)K(\mathbb Z,3), or it has infinitely many non-trivial homotopy groups and kk-invariants. Relying on recent advances in the theory of HH-spaces, we then show that simply connected HH-spaces whose mod 22 cohomology is finitely generated as an algebra over the Steenrod algebra do not have homology exponents, except products of mod 22 finite HH-spaces with copies of CP\mathbb C P^\infty and K(Z,3)K(\mathbb Z,3).

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

DOI 10.4171/RMI/562