English

Loop Products and Closed Geodesics

Algebraic Topology 2019-12-19 v1 Differential Geometry

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.

Cite

@article{arxiv.0707.3486,
  title  = {Loop Products and Closed Geodesics},
  author = {Mark Goresky and Nancy Hingston},
  journal= {arXiv preprint arXiv:0707.3486},
  year   = {2019}
}

Comments

63 pages

R2 v1 2026-06-21T09:01:07.781Z