DOI QR코드

DOI QR Code

SOME COHOMOTOPY GROUPS OF SUSPENDED QUATERNIONIC PROJECTIVE PLANES

  • Received : 2015.10.14
  • Published : 2016.09.30

Abstract

In this paper we present the computation of two kinds of cohomotopy groups $[{\Sigma}^n+^4{\mathbb{H}}P^2,S^n]$ and $[{\Sigma}^n+^5{\mathbb{H}}P^2,S^n]$ for a non-negative integer n, where ${\Sigma}^k{\mathbb{H}}P^2$ is the k-fold suspension of quaternionic projec- tive plane ${\mathbb{H}}P^2$.

Keywords

Acknowledgement

Supported by : Korea University

References

  1. K. Aoki, On torus cohomotopy groups, Proc. Japan Acad. 30 (1954), 694-697. https://doi.org/10.3792/pja/1195525964
  2. H. Kachi, J. Mukai, T. Nozaki, Y. Sumita, and D. Tamaki, Some cohomotopy groups of suspended projective planes, Math. J. Okayama Univ. 43 (2001), 105-121.
  3. S. Kikkawa, J. Mukai, and D. Takaba, Cohomotopy sets of projective planes, J. Fac. Sci. Shinshu Univ. 33 (1998), no. 1, 1-7.
  4. K. Oguchi, Generators of 2-primary components of homotopy groups of spheres, unitary groups and symplectic groups, J. Fac. Sci. Univ. Tokyo Sect. I 11 (1964), 65-111.
  5. H. Oshima and Koji Takahara, Cohomotopy of Lie groups, Osaka J. Math. 28 (1991), no. 2, 213-221.
  6. R. Rubinsztein, Some remarks on the cohomotopy of $\mathbb{Z}P^{\infty},$, Quart. J. Math. Oxford Ser. (2) 30 (1979), no. 117, 119-128. https://doi.org/10.1093/qmath/30.1.119
  7. Y. Sumita, Master's thesis, Shinshu University, 1998.
  8. H. Toda, Composition methods in homotopy groups of spheres, Annals of Mathematics Studies, No. 49, Princeton University Press, Princeton, N.J. 1962.