English

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

Algebraic Topology 2025-09-24 v8

Abstract

In this paper, we determined the 2,32,3-components of the homotopy groups πr+k(ΣkHP2)\pi _{r+k}(\Sigma ^{k}\mathbb{H}P^{2}) for all 7r15 7\leq r\leq15 and all   k0\;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 HP3\mathbb{H} P^{3} localized at 3 , and the decompositions of the suspended self smashes.

Keywords

Cite

@article{arxiv.2301.06776,
  title  = {On the Homotopy Groups of the Suspended Quaternionic Projective Plane and Applications},
  author = {Juxin Yang and Juno Mukai and Jie Wu},
  journal= {arXiv preprint arXiv:2301.06776},
  year   = {2025}
}