Transferring homotopy commutative algebraic structures

We show that the sum over planar tree formula of Kontsevich and Soibelman transfers C∞C∞-structures along a contraction. Applying this result to a cosimplicial commutative algebra A
• A
• over a field of characteristic zero, we exhibit a canonical C∞C∞-structure on Tot(A
• )Tot(A
• ), which is unital if A
• A
• is; in particular, we obtain a canonical C∞C∞-structure on the cochain complex of a simplicial set.