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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the equivariant Morse complex of
the free loop space of a surface


Author: Nancy Hingston
Journal: Trans. Amer. Math. Soc. 350 (1998), 1129-1141
MSC (1991): Primary 58E10; Secondary 57R91, 53C22
MathSciNet review: 1458305
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Abstract: We prove two theorems about the equivariant topology of the free loop space of a surface. The first deals with the nondegenerate case and says that the ``ordinary'' Morse complex can be given an $O(2)$-action in such a way that it carries the $O(2)$-homotopy type of the free loop space. The second says that, in terms of topology, the iterates of an isolated degenerate closed geodesic ``look like'' the continuous limit of the iterates of a finite, fixed number of nondegenerate closed geodesics.


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Additional Information

Nancy Hingston
Affiliation: Department of Mathematics, The College of New Jersey, P. O. Box 7718, Ewing, New Jersey 08628-0718
Email: hingston@tcnj.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02097-2
PII: S 0002-9947(98)02097-2
Received by editor(s): May 4, 1996
Article copyright: © Copyright 1998 American Mathematical Society