### Abstract

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 language | English |
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Pages (from-to) | 963-980 |

Journal | Revista Matematica Iberoamericana |

Volume | 24 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jan 2008 |

### Keywords

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

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## Cite this

Clément, A., & Scherer, J. (2008). Homology exponents for H-spaces.

*Revista Matematica Iberoamericana*,*24*(3), 963-980. https://doi.org/10.4171/RMI/562