2003/09/28 by Thomas Tradler, Tradler, Thomas, Mahmoud Zeinalian +3
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.math/0309455
openalex publication_date 2003/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the complex C_\bullet X of rational simplicial chains on a compact and triangulated Poincaré duality space X of dimension d is an A_∞ coalgebra with ∞ duality. This is the structure required for an A_∞ version of the cyclic Deligne conjecture. One corollary is that the shifted Hochschild cohomology HH\bullet+d (C^\bullet X, C_\bullet X) of the cochain algebra C^\bullet X with values in C_\bullet X has a BV structure. This implies, if X is moreover simply connected, that the shifted homology H\bullet+dLX of the free loop space admits a BV structure. An appendix by Dennis Sullivan gives a general local construction of ∞ structures.