Loop Products and Closed Geodesics

2007/07/24 by Mark Goresky, Nancy Hingston · 1 citation
Mathematics · #math.AT #math.DG #msc:55N45 #msc:53C22 #msc:37B30

paper · pdf · doi:10.1215/00127094-2009-049

published as Duke Math. J. 150, no. 1 (2009), 117-209 · 63 pages

arxiv created 2007/07/24 · arxiv updated 2019/12/19

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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