# The Hurewicz image of the $\eta_i$ family

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

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\$.