## Advanced Studies in Pure Mathematics

### Fundamental Groups of Semisimple Symmetric Spaces

Jiro Sekiguchi

#### Abstract

The aim of this report is to determine the fundamental group of an arbitrary irreducible semisimple symmetric space $G/H$ when $G$ is a connected semisimple Lie group with trivial center. The fundamental group $\pi_1(G/H)$ is well-known if $G/H$ is Riemannian. Therefore, we restrict our attention to the case where $G/H$ is non-Riemannian so both $G$ and $H$ are not compact. The result is summarized in Table 4.

#### Article information

Dates
First available in Project Euclid: 31 May 2018

https://projecteuclid.org/ euclid.aspm/1527733110

Digital Object Identifier
doi:10.2969/aspm/01410519

Mathematical Reviews number (MathSciNet)
MR1039850

Zentralblatt MATH identifier
0723.22021

#### Citation

Sekiguchi, Jiro. Fundamental Groups of Semisimple Symmetric Spaces. Representations of Lie Groups, Kyoto, Hiroshima, 1986, 519--529, Mathematical Society of Japan, Tokyo, Japan, 1988. doi:10.2969/aspm/01410519. https://projecteuclid.org/euclid.aspm/1527733110