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

Hingston, Nancy

doi:10.1090/S0002-9947-98-02097-2

On the equivariant Morse complex of the free loop space of a surface
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Trans. Amer. Math. Soc. 350 (1998), 1129-1141 Request permission

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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