2019/12/31 by Manuel Rivera, Rivera, Manuel, Zhengfang Wang +1
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1912.13267
openalex publication_date 2019/12/31 · openalex created_date 2022/12/20 · openalex updated_date 2026/07/28
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.