 On the Hochschild and Harrison (co)homology of C ∞-algebras and applications to string topologyGrégory Ginot A chapter in Deformation Spaces, 2010, pp 1-51 from Springer Abstract: 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 Poincaré-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. Keywords: Spectral Sequence; String Topology; Commutative Algebra; Algebra Structure; Hochschild Cohomology (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-8348-9680-3_1 Ordering information: This item can be ordered from DOI: 10.1007/978-3-8348-9680-3_1 Access Statistics for this chapter More chapters in Springer Books from Springer |
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