Dimension of asymptotic cones of Lie groups

By Yves Cornulier. 2007

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We compute the covering dimension of 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 nonpositively curved metric space.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/63056c8bdf13f4e7905fd3b2c1fd6acd6ae6365a