Tautological formal Frobenius manifold structures on a Frobenius algebra

Abstract

We give some tautological constructions of formal Frobenius manifold structures on a Frobenius algebra. As a consequence, one can construct a version of "quantum cohomology" for any connected oriented closed manifold, in the sense that it is a deformation given by a function which satisfies the WDVV equations. We compute the potential functions for complex projective spaces.