A Morse theoretic description of the Goresky-Hingston product

TL;DR

This paper provides a Morse theoretic framework for the Goresky-Hingston coproduct, establishing its homotopy invariance and linking it to Floer homology of cotangent bundles.

Contribution

It introduces a Morse theoretic description of the coproduct and demonstrates its homotopy invariance, connecting it to Floer homology.

Findings

Morse theoretic description of the coproduct

Homotopy invariance of the coproduct

Connection to Floer homology of cotangent bundles

Abstract

The Goresky-Hingston coproduct was first introduced by D. Sullivan and later extended by M. Goresky and N. Hingston. In this article we give a Morse theoretic description of the coproduct. Using the description we prove homotopy invariance property of the coproduct. We describe a connection between our Morse theoretic coproduct and a coproduct on Floer homology of cotangent bundle.