In this paper, we determined the $2,3$-components of the homotopy groups $\pi _{ r+k}(\Sigma ^{ k}\mathbb{ H}P^{ 2})$ for all $ 7\leq r\leq15$ and all $\;k\geq0$, especially for the unstable ones. And we gave the applications, including the classification theorems of the 1-connected CW complexes having CW types of the suspended $\mathbb{ H} P^{ 3}$ localized at 3 , and the decompositions of the suspended self smashes.
Categories: math.AT