Eccles, Peter J. and Zare, Hadi
(2011)
*The Hurewicz image of the $\eta_i$ family.*
[MIMS Preprint]

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## Abstract

We consider the problem of detecting Mahowald's family $\eta_i \in 2 \pi^{S}_{2^i} in homology. This allows us to identify specic spherical classes in $H_* \Omega_0^{2^{i+1} - 8 + k}S^{2^i-2}$ for $0 \leq k \leq 6$. We then identify the type of the subalgebras that these classes give rise to, and calculate the $A$-module and $R$-module structure of these subalgebras. We shall the discuss the relation of these calculations to the Curtis conjecture on spherical classes in $H_* Q_0S^0$.

Item Type: | MIMS Preprint |
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Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 55 Algebraic topology |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 14 Jan 2011 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1561 |

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