In this paper, we show that the Chas-Sullivan product (respectively the
Goresky-Hingston product) on level homology detects isolated closed geodesic
with slowest (resp. fastest) possible index growth rate. We discuss how string
topology along with this result gives a new perspective on questions of the
existence of closed geodesics.Comment: 9 page

Maiti, Arun

English

arXiv

In this paper, we show that the Chas-Sullivan product (respectively the
Goresky-Hingston product) on level homology detects isolated closed geodesic
with slowest (resp. fastest) possible index growth rate. We discuss how string
topology along with this result gives a new perspective on questions of the
existence of closed geodesics.Comment: This work will be included as a part of a joint work with another
  author. The joint work will be submitted soo

The closed geodesic problem and the string products

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