  The category of differential graded operads is a cofibrantly generated model
category and as such inherits simplicial mapping spaces. The vertices of an
operad mapping space are just operad morphisms. The 1-simplices represent
homotopies between morphisms in the category of operads.
  The goal of this paper is to determine the homotopy of the operadic mapping
spaces Map(E_n,C) with a cofibrant E_n-operad on the source and the commutative
operad on the target. First, we prove that the homotopy class of a morphism
phi: E_n -> C is uniquely determined by a multiplicative constant which gives
the action of phi on generating operations in homology. From this result, we
deduce that the connected components of Map(E_n,C) are in bijection with the
ground ring. Then we prove that each of these connected components is
contractible.
  In the case where n is infinite, we deduce from our results that the space of
homotopy self-equivalences of an E-infinity-operad in differential graded
modules has contractible connected components indexed by invertible elements of
the ground ring.
