Tautological formal Frobenius manifold structures on a Frobenius algebra

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.

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Published 1 January 2000