## 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