2024/03/12 by Manuel Rivera, Rivera, Manuel, Daniel Tolosa +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)
paper · pdf · doi:10.48550/arxiv.2403.08116
openalex publication_date 2024/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the cyclic chain complex of the categorical coalgebra of singular chains on an arbitrary topological space X is naturally quasi-isomorphic to the S1-equivariant chains of the free loop space of X. This statement does not require any hypotheses on X or on the commutative ring of coefficients. Along the way, we introduce a family of polytopes, coined as Goodwillie polytopes, that controls the combinatorics behind the relationship of the coHochschild complex of a categorical coalgebra and the Hochschild complex of its associated differential graded category.