Transferring homotopy commutative algebraic structures

We show that the sum over planar tree formula of Kontsevich and Soibelman transfers C-infinity-structures along a contraction. Applying this result to a cosimplicial commutative algebra A(center dot) over a field of characteristic zero, we exhibit a canonical C-infinity-structure on Tot(A(center dot)), which is unital if A(center dot) is; in particular, we obtain a canonical C-infinity-structure on the cochain complex of a simplicial set. (C) 2008 Elsevier B.V. All rights reserved.