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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Geometrizing Infinite Dimensional Locally Compact Groups
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by Conrad Plaut PDF
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.
References
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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
  • Received by editor(s): February 16, 1994
  • Additional Notes: The author gratefully acknowledges the support of NSF grant DMS-9401302
  • © Copyright 1996 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 348 (1996), 941-962
  • MSC (1991): Primary 53C70, 22D05; Secondary 22E65
  • DOI: https://doi.org/10.1090/S0002-9947-96-01592-9
  • MathSciNet review: 1348156