Non-commutative calculus and Getzler-Gauss-Manin connections for Open-closed Homotopy Algebras

Abstract

We establish the calculus structure on Hochschild invariants of open-closed homotopy algebras. We further define the Getzler-Gauss-Manin connection and show that it is flat up to chain homotopy on the open-closed periodic cyclic chain complex.

22 pages. v2: an error corrected. Comments welcome