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Geometrizing Infinite Dimensional Locally Compact Groups
Author(s):
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
Email:
plaut@novell.math.utk.edu
DOI:
10.1090/S0002-9947-96-01592-9
PII:
S 0002-9947(96)01592-9
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
Copyright of article:
Copyright
1996,
American Mathematical Society
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