Fundamental Groups of Semisimple Symmetric Spaces

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.