Isometry groups of non-positively curved spaces: structure theory

TL;DR

This paper develops the structure theory of isometry groups of non-positively curved spaces, focusing on decompositions, subgroup structures, and characterizations of symmetric spaces and buildings.

Contribution

It introduces new structural insights into isometry groups of non-positively curved spaces, including decompositions and subgroup characterizations.

Findings

Decomposition theorems for isometry groups

Characterization of symmetric spaces and Bruhat--Tits buildings

Analysis of normal subgroup structures

Abstract

We develop the structure theory of full isometry groups of locally compact non-positively curved metric spaces. Amongst the discussed themes are de Rham decompositions, normal subgroup structure and characterising properties of symmetric spaces and Bruhat--Tits buildings. Applications to discrete groups and further developments on non-positively curved lattices are exposed in a companion paper: "Isometry groups of non-positively curved spaces: discrete subgroups".