On the Homotopy Groups of the Suspended Quaternionic Projective Plane and Applications

Abstract

In this paper, we determined the $2,3$-components of the homotopy groups ${\pi }_{r+k}({\Sigma }^k\mathbb{H}{P}^2)$ for all $7\le r\le 15$ and all $k\ge 0$, 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.