Geometrizing Infinite Dimensional Locally Compact Groups

Plaut, Conrad

doi:10.1090/S0002-9947-96-01592-9

Geometrizing Infinite Dimensional Locally Compact Groups
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Trans. Amer. Math. Soc. 348 (1996), 941-962 Request permission

Abstract:

We study groups having invariant metrics of curvature bounded below in the sense of Alexandrov. Such groups are a generalization of Lie groups with invariant Riemannian metrics, but form a much larger class. We prove that every locally compact, arcwise connected, first countable group has such a metric. These groups may not be (even infinite dimensional) manifolds. We show a number of relationships between the algebraic and geometric structures of groups equipped with such metrics. Many results do not require local compactness.

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