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Dimension of asymptotic cones of Lie groups

Yves de Cornulier
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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.

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Yves de Cornulier. 2007-03-07. Dimension of asymptotic cones of Lie groups. https://doi.org/10.1112/jtopol%2Fjtm013

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