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- W2184206199 abstract "We study Hochschild (co)homology of commutative and associative up to homotopy algebras with coefficient in a homotopy analogue of symmetric bimodules. We prove that Hochschild (co)homology is equipped with λ-operations and Hodge decomposition generalizing the results in [GS1] and [Lo1] for strict algebras. The main application is concerned with string topology: we obtain a Hodge decomposition compatible with a non-trivial BV-structure on the homology H *(LX) of the free loop space of a triangulated Poincare-duality space. Harrison (co)homology of commutative and associative up to homotopy algebras can be defined similarly and is related to the weight 1 piece of the Hodge decomposition. We study Jacobi-Zariski exact sequence for this theory in characteristic zero. In particular, we define (co)homology of relative A ∞-algebras, i.e., A ∞-algebras with a C ∞-algebra playing the role of the ground ring. We also give a relation between the Hodge decomposition and homotopy Poisson-algebras cohomology." @default.
- W2184206199 created "2016-06-24" @default.
- W2184206199 creator A5085694048 @default.
- W2184206199 date "2010-01-01" @default.
- W2184206199 modified "2023-09-26" @default.
- W2184206199 title "On the Hochschild and Harrison (co)homology of C ∞-algebras and applications to string topology" @default.
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