Title: Homology exponents for H-spaces
Authors: Alain Clement and Jerome Scherer
Abstract: 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 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, 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).
arXiv submission number: AT/0612276