Pre-Calabi-Yau algebras and oriented gravity properad

2025/01/19 by Sergei Merkulov, Merkulov, Sergei
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2501.11158

openalex publication_date 2025/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the dual cyclic Hochschild complex Cyc^\bullet(A,\mathbbK) of a (possibly, infinite-dimensional) A_∞-algebra (A,μ) and prove that any pre-Calabi-Yau extension π of the given A_∞ structure μ in A induces on the cyclic cohomology of (A,μ) a representation of a new dg properad of oriented ribbon graphs. We compute the cohomology of that properad in terms of the compactly supported cohomology groups of moduli spaces M_g,m+n of algebraic curves of genus g with m+n marked points. We also show that the gravity operad acts naturally on the higher Hochschild cohomology of any pre-CY algebra (A, π).

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