Invariance of the Goresky-Hingston algebra on reduced Hochschild homology

Abstract

We prove that two quasi-isomorphic simply connected differential graded associative Frobenius algebras have isomorphic Goresky-Hingston algebras on their reduced Hochschild homology. Our proof is based on relating the Goresky-Hingston algebra on reduced Hochschild homology to the singular Hochschild cohomology algebra. For any simply connected oriented closed manifold M of dimension k, the Goresky-Hingston algebra on reduced Hochschild homology induces an algebra structure of degree k−1 on H * (LM ; Q), the reduced rational cohomology of the free loop space of M . As a consequence of our algebraic result, we deduce that the isomorphism class of the induced algebra structure on H * (LM ; Q) is an invariant of the homotopy type of M .