# Homology exponents for H-spaces

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Version: Author's accepted manuscript

Version: Author's accepted manuscript

Serval ID

serval:BIB_1BADBC6A2BC8

Type

**Article**: article from journal or magazin.

Collection

Publications

Fund

Title

Homology exponents for H-spaces

Journal

Revista Matemática Iberoamericana

ISSN

0213-2230

Publication state

Published

Issued date

2008

Peer-reviewed

Oui

Volume

24

Pages

963-980

Language

english

Notes

Actas del "XVI Coloquio Latinoamericano de Algebra" (Colonia, Uruguay, 2005), 1-19

Abstract

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 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 $B\Z/2^r$, $S^1$, $\CP^\infty$, and $K(\Z,3)$, 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 $\CP^\infty$ and $K(\Z,3)$.

Keywords

Homology exponent, H-space, loop space, Steenrod algebra

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09/06/2010 11:22

Last modification date

03/03/2018 13:31