Homology exponents for H-spaces

Details Homology exponents for H-spaces Homology exponents for H-spaces

2006-12-11

arxiv.org/abs/math/0612276v1

Mathematics

Algebraic Topology

12 pages

Scientific paper

We say that a space X admits a homology exponent if there exists an exponent for the torsion subgroup of the integral homology. 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, K(Z, 2), 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 K(Z, 2) and K(Z,3).

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