Algebraic structures of $F$-manifolds via pre-Lie algebras (1706.07340v2)

Abstract: We relate the operad FMan controlling the algebraic structure on the tangent sheaf of an $F$-manifold (weak Frobenius manifold) defined by Hertling and Manin to the operad PreLie of pre-Lie algebras: for the filtration of PreLie by powers of the ideal generated by the Lie bracket, the associated graded object is FMan.