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arXiv · 0707.3486

Loop Products and Closed Geodesics

Mark Goresky·Nancy Hingston
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Abstract

We show the Chas-Sullivan product (on the homology of the free loop space of a Riemannian manifold) is related to the Morse index of its closed geodesics. We construct related products in the cohomology of the free loop space and of the based loop space, and show they are nontrivial.

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Mark Goresky, Nancy Hingston. 2007-07-24. Loop Products and Closed Geodesics. https://doi.org/10.1215/00127094-2009-049

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