The Functor $A^{\min}$ for $(p-1)$-cell Complexes and $\EHP$ Sequences

Let $X$ be a co-$H$-space of $(p-1)$-cell complex with all cells in even dimensions. Then the loop space $\Omega X$ admits a retract $\bar A^{\min}(X)$ that is the evaluation of the functor $\bar A^{\min}$ on $X$. In this paper, we determine the homology $H_*(\bar A^{\min}(X))$ and give the $\EHP$ sequence for the spaces $\bar A^{\min}(X)$.