## Tsukuba Journal of Mathematics

### A remark on the second homotopy groups of compact Riemannian 3-symmetric spaces

Takashi Koda

#### Abstract

In order to calculate the second Stiefel-Whitney class of a l-connected compact Riemannian 3-symmetric space $G/K$ by BorelHirzebruch's method, we have to know the second cohomology group $H^{2}(G/K, Z_{2})\cong Hom(\pi_{2}(G/K), Z_{2})$. In this paper, we shall describe precisely the connected Lie subgroup $K$ and calculate explicitly the second homotopy group $\pi_{2}(G/K)$ in terms of the roots of $G$.

#### Article information

Source
Tsukuba J. Math., Volume 18, Number 1 (1994), 145-163.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496162461

Digital Object Identifier
doi:10.21099/tkbjm/1496162461

Mathematical Reviews number (MathSciNet)
MR1287836

Zentralblatt MATH identifier
0842.57021

#### Citation

Koda, Takashi. A remark on the second homotopy groups of compact Riemannian 3-symmetric spaces. Tsukuba J. Math. 18 (1994), no. 1, 145--163. doi:10.21099/tkbjm/1496162461. https://projecteuclid.org/euclid.tkbjm/1496162461