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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Exponential maps of Sobolev metrics
on loop groups


Author: Gerard Misiolek
Journal: Proc. Amer. Math. Soc. 127 (1999), 2475-2482
MSC (1991): Primary 58B20; Secondary 22E65
DOI: https://doi.org/10.1090/S0002-9939-99-05063-7
Published electronically: April 15, 1999
MathSciNet review: 1626450
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Abstract: We find conditions for the exponential map on a weak riemannian Hilbert manifold to be a nonlinear Fredholm map of index zero and apply the result to left-invariant Sobolev metrics on loop groups.


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Additional Information

Gerard Misiolek
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: misiolek@math.nd.edu

DOI: https://doi.org/10.1090/S0002-9939-99-05063-7
Keywords: Exponential map, Fredholm operators, loop groups
Received by editor(s): November 3, 1997
Published electronically: April 15, 1999
Communicated by: Józef Dodziuk
Article copyright: © Copyright 1999 American Mathematical Society