An action of the Polishchuk differential operator via punctured surfaces

For a family of Jacobians of smooth pointed curves, there is a notion of tautological algebra. There is an action of sl2 on this algebra. We define and study a lifting of the Polishchuk operator, corresponding to f ∈sl2, on an algebra consisting of punctured Riemann surfaces. As an application, we compare a class of tautological relations on moduli of curves, discovered by Faber and Zagier and relations on the universal Jacobian. We prove that the so called top Faber-Zagier relations come from a class of relations on the Jacobian side.