Group completions and orbifolds of variable negative curvature

Abstract:

W. J. Floyd’s comparison of the Furstenberg maximal boundary of a noncompact, ${\mathbf {R}}$-rank one, connected semisimple Lie group $G$ with finite center and the group completion of a discrete, cocompact subgroup $\Gamma$ of $G$ is extended to a homeomorphism between the group completion of the fundamental group $\Gamma$ of a closed Riemannian orbifold $M = \Gamma \backslash X$ of strictly negative sectional curvatures and the sphere at infinity in the Eberlein-O’Neill compactification $\overline X$ of the universal cover $X$ of $M$.