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Journal of Topology Advance Access published online on February 6, 2008
Journal of Topology, doi:10.1112/jtopol/jtm013
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© 2008 London Mathematical Society

Dimension of asymptotic cones of Lie groups

Yves de Cornulier

IRMAR, Campus de Beaulieu, 35042 Rennes Cedex, France cornulier{at}phare.normalesup.org


  Abstract

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.

Received February 6, 2007.

2000 Mathematics Subject Classification 22E15 (primary), 20F69, 22E25, 54F45 (secondary)


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