Homology exponents for \(H\)-spaces. (English) Zbl 1160.57034
In this paper, a space \(X\) admits a homology exponent if there exists an integer \(k\) such that \(2^k. T_2 H^*(X;{\mathbb Z})=0\), where \(T_2\) is the 2-torsion subgroup. The authors study connected \(H\)-spaces \(X\) of finite type which admits a homology exponent. They prove that – \(X\) is, up to 2-completion, a product of spaces of the form \(B{\mathbb Z}/2^r\), \(S^1\), \({\mathbb C}P^{\infty}\) and \(K({\mathbb Z},3)\) or \(X\) admit infinitely many non-trivial homotopy groups and \(k\)-invariants – if \(X\) is simply connected and \(H^*(X;F_2)\) finitely generated as an algebra over the Steenrod algebra, then \(X\) is, up to 2-completion, the product of a mod 2 finite \(H\)-space with copies of \({\mathbb C}P^{\infty}\) and \(K({\mathbb Z},3)\).
Reviewer: Daniel Tanré (Villeneuve d’ Ascq)
MSC:
| 57T25 | Homology and cohomology of \(H\)-spaces |
| 55S45 | Postnikov systems, \(k\)-invariants |
| 55P20 | Eilenberg-Mac Lane spaces |
| 55S10 | Steenrod algebra |
| 55T10 | Serre spectral sequences |
| 55T20 | Eilenberg-Moore spectral sequences |
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