Dimension of asymptotic cones of Lie groups

Abstract

We compute the covering dimension the asymptotic cone of a connected Lie group. For simply connected solvable Lie groups, this is the codimension of the exponential radical. As an application of the proof, we give a characterization of connected Lie groups that quasi-isometrically embed into a non-positively curved metric space.

22 pages, 0 figure

References in corpus (5)

• Kazhdan and Haagerup Properties in algebraic groups over local fields
• Lacunary hyperbolic groups
• Dimension and rank for mapping class groups
• Connected Lie groups and property RD
• On Asymptotic Assouad-Nagata Dimension

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• Embedding relatively hyperbolic groups in products of trees
• From the geometry of box spaces to the geometry and measured couplings of groups
• Geometric presentations of Lie groups and their Dehn functions
• Poincaré profiles of Lie groups and a coarse geometric dichotomy
• Sublinear quasiconformality and the large-scale geometry of Heintze groups
• Large-scale sublinearly Lipschitz geometry of hyperbolic spaces
• Local topological properties of asymptotic cones of groups
• Length functions exponentially distorted on subgroups of complex Lie groups
• Residual finiteness and strict distortion of cyclic subgroups of solvable groups
• Property (QT) for 3-manifold groups
• On sublinear bilipschitz equivalence of groups
• The divergence of the special linear group over a function ring
• On the logarithmic coarse structures of Lie groups and hyperbolic spaces