# Some computations in string topology

## TL;DR

This paper explores Hochschild chain models to simplify computations in string topology, introduces new observations, and discusses how certain homology classes detect closed geodesics with optimal index growth.

## Contribution

It provides new Hochschild chain models for string topology operations and links local homology classes to the detection of closed geodesics.

## Key findings

- Hochschild models simplify string topology computations
- Nonnilpotent local homology classes detect closed geodesics
- Optimal index growth rates are achieved in certain homology classes

## Abstract

In this paper, we discuss Hochschild chain models for some of the string topology operations. We use these models to simplify the proofs and computations of some of the results in string topology. Along the way we also make some new observations. We further discuss how nonnilpotent local level homology classes with respect to the Chas-Sullivan and the Goresky-Hingston product detect closed geodesics with optimal index growth rates.