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Homology exponents for H-spaces | | Alain Clement
; Jerome Scherer
; | | Date: |
11 Dec 2006 | | Subject: | Algebraic Topology | | 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 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). | | Source: | arXiv, math/0612276 | | Services: | Forum | Review | PDF | Favorites | |
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