Dimension of asymptotic cones of Lie groups

We compute the covering dimension of the asymptotic cone ofa 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 ofconnected Lie groups that quasi-isometrically embed into a nonpositivelycurved metric space. Received February 6, 2007.