The product structure on loop homology

Abstract

In this paper, we survey the result of R. Cohen and J. Jones on the Chas-Sullivan product.

Briefly, Cohen and Jones precisely defined the Chas-Sullivan product using ring spectra,

and show that the Chas-Sullivan product coincides with the cup product structure on the

Hochschild cohomology of the cochain complex of the base manifold. In the sequel paper,

they introduce a loop homology spectral sequence and compute the algebra structure on

the free loop space of spheres and complex projective spaces.