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Transactions of the American Mathematical Society

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Geometrizing Infinite Dimensional Locally Compact Groups

Author: Conrad Plaut
Journal: Trans. Amer. Math. Soc. 348 (1996), 941-962
MSC (1991): Primary 53C70, 22D05; Secondary 22E65
MathSciNet review: 1348156
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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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Additional Information

Conrad Plaut
Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300

Keywords: Locally compact groups, Alexandrov curvature, invariant metric
Received by editor(s): February 16, 1994
Additional Notes: The author gratefully acknowledges the support of NSF grant DMS-9401302
Article copyright: © Copyright 1996 American Mathematical Society