Isometry groups of non-positively curved spaces: structure theory

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".

The original version (September 2, 2008) has been split into two articles. This is the first part; the second is available as of today on the arxiv under the title: "Isometry groups of non-positively curved spaces: discrete subgroups"

References in corpus (3)

• At infinity of finite-dimensional CAT(0) spaces
• Isometry groups of non-positively curved spaces: discrete subgroups
• On lengths on semisimple groups

Cited by in corpus (28)

• Rank rigidity for CAT(0) cube complexes
• Hierarchically hyperbolic spaces I: curve complexes for cubical groups
• Decomposing locally compact groups into simple pieces
• At infinity of finite-dimensional CAT(0) spaces
• Isometry groups of non-positively curved spaces: discrete subgroups
• Rank-one isometries of proper CAT(0)-spaces
• Fixed points and amenability in non-positive curvature
• Quasi-isometric classification of right-angled Artin groups I: the finite out case
• Gelfand pairs and strong transitivity for Euclidean buildings
• A lattice in more than two Kac--Moody groups is arithmetic
• Invariant random subgroups of linear groups
• Infinite dimensional non-positively curved symmetric spaces of finite rank
• Lattices in a product of trees, hierarchically hyperbolic groups, and virtual torsion-freeness
• Superrigidity of actions on finite rank median spaces
• Geometric density for invariant random subgroups of groups acting on CAT(0) spaces
• On the structure and arithmeticity of lattice envelopes
• Isometry groups of proper CAT(0)-spaces
• Furstenberg Maps For CAT(0) Targets Of Finite Telescopic Dimension
• L2-invariants of nonuniform lattices in semisimple Lie groups
• Erratum and addenda to "Isometry groups of non-positively curved spaces: discrete subgroups"
• CAT(0) spaces with boundary the join of two Cantor sets
• Obstructions to nonpositive curvature for open manifolds
• Groups acting on spaces of non-positive curvature
• Isomorphisms of unitary forms of Kac-Moody groups over finite fields
• Finite cuts and CAT(0) boundaries
• Representations of infinite dimension orthogonal groups of quadratic forms with finite index
• Affine Maps Between CAT(0) Spaces
• Proper CAT(0) actions of unipotent-free linear groups