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

TL;DR

This paper computes specific homotopy groups of the suspended quaternionic projective plane and applies these results to classify certain CW complexes and decompose suspended self-smashes.

Contribution

It determines the 2,3-components of homotopy groups of suspended quaternionic projective planes for a range of dimensions, especially in unstable cases, and applies these to classification and decomposition problems.

Findings

Computed homotopy groups for 7 ≤ r ≤ 15 and all k ≥ 0.

Provided classification theorems for CW complexes with suspended quaternionic projective space types.

Achieved decompositions of suspended self-smashes.

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\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.