Pre-Calabi-Yau extensions of A∞ algebras induce actions of a newly constructed dg properad of oriented ribbon graphs on cyclic Hochschild cohomology, whose cohomology matches compactly supported cohomology of moduli spaces of curves.
Pre-CalabiYau algebras as noncommutative Poisson structures , Journal of Algebra 567 (2021), pp
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Pre-Calabi-Yau algebras and oriented gravity properad
Pre-Calabi-Yau extensions of A∞ algebras induce actions of a newly constructed dg properad of oriented ribbon graphs on cyclic Hochschild cohomology, whose cohomology matches compactly supported cohomology of moduli spaces of curves.