Open Access
November, 2008 Homology exponents for $H$-spaces
Alain Clément , Jérôme Scherer
Rev. Mat. Iberoamericana 24(3): 963-980 (November, 2008).


We say that a space $X$ admits a \emph{homology exponent} if there exists an exponent for the torsion subgroup of $H^*(X;\mathbb Z)$. 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 $B\mathbb Z/2^r$, $S^1$, $\mathbb C P^\infty$, and $K(\mathbb Z,3)$, 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 $\mathbb C P^\infty$ and $K(\mathbb Z,3)$.


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Alain Clément . Jérôme Scherer . "Homology exponents for $H$-spaces." Rev. Mat. Iberoamericana 24 (3) 963 - 980, November, 2008.


Published: November, 2008
First available in Project Euclid: 9 December 2008

zbMATH: 1160.57034
MathSciNet: MR2490205

Primary: 55S45 , 57T25
Secondary: 55P20 , 55S10 , 55T10 , 55T20

Keywords: $H$-space , homology exponent , loop space , Steenrod algebra

Rights: Copyright © 2008 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.24 • No. 3 • November, 2008
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