Compactification de Chabauty des espaces sym\'etriques de type non compact

TL;DR

This paper explores the Chabauty compactification of noncompact symmetric spaces, describing boundary subgroups using simplified methods, enhancing understanding of the space's topological and geometric structure.

Contribution

It provides a new, simpler description of the boundary subgroups in the Chabauty compactification of noncompact symmetric spaces.

Findings

Identification of boundary subgroups in the compactification

Simplified proof techniques compared to prior work

Enhanced understanding of the topology of symmetric spaces

Abstract

The space of closed subgroups of a locally compact topological group is endowed with a natural topology, called the Chabauty topology. Let X be a symmetric space of noncompact type, and G be its group of isometries. The space X identifies with the subspace of maximal compact subgroups of G : taking the closure gives rise to the Chabauty compactification of the symmetric space X. Using simpler arguments than those present in the book of Guivarc'h, Ji and Taylor, we describe the subgroups that appear in the boundary of the compactification.