The Path-product in Morse Homology with differential graded coefficients

Abstract

We will use the tools developed in the article [5] to give a Morse-theoretical description of a string topology product on the homology of the space of paths in a manifold Y with endpoints in a submanifold X and a module structure on this homology over the Chas–Sullivan ring of Y . These operations have been defined and studied by Stegemeyer in [6] in singular homology.