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We introduce and study the notion of a dual Feynman transform of a modularoperad. This generalizes and gives a conceptual explanation of Kontsevich'sdual construction producing graph cohomology classes from a contractibledifferential graded Frobenius algebra. The dual Feynman transform of a modularoperad is indeed linear dual to the Feynman transform introduced by Getzler andKapranov when evaluated on vacuum graphs. In marked contrast to the Feynmantransform, the dual notion admits an extremely simple presentation viagenerators and relations; this leads to an explicit and easy description of itsalgebras. We discuss a further generalization of the dual Feynman transformwhose algebras are not necessarily contractible. This naturally gives rise to atwo-colored graph complex analogous to the Boardman-Vogt topological treecomplex.

Dual Feynman transform for modular operads