Free frobenius algebra on the differential forms of a manifold

Abstract

We construct an action of a free resolution of the Frobenius properad on the differential forms of a closed oriented manifold. As a consequence, the forms of a manifold with values in a semi-simple Lie algebra have an additional structure given by an action of a free resolution of the properad describing Lie di-algebras with module compatibility.

This paper has been withdrawn by the author. The definition given for the Frobenius properad is incorrect, i.e. what is stated is not a properad. For sign reasons following from the permutation group actions, in odd degree n, there should be no positive genus operations. The error in that definition invalidates the proof of the main claim in Theorem 4 (even for a proper definition of Frobenius properad). Theorem 8 is also affected similarly