Open-closed homotopy algebras admit a non-commutative calculus on their Hochschild invariants and a Getzler-Gauss-Manin connection on their periodic cyclic complex, flat up to chain homotopy.
Introduction to A-infinity algebras and modules
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These are expanded notes of four introductory talks on A-infinity algebras, their modules and their derived categories.
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Non-commutative calculus and Getzler-Gauss-Manin connections for Open-closed Homotopy Algebras
Open-closed homotopy algebras admit a non-commutative calculus on their Hochschild invariants and a Getzler-Gauss-Manin connection on their periodic cyclic complex, flat up to chain homotopy.