Alain Clément and Jérôme Scherer
نویسندگان
چکیده
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 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 , S 1 , CP ∞ , and K(Z, 3), or it has infinitely many non-trivial homotopy groups and k-invariants. We then show with the same methods 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).
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