  A quasi-Poisson manifold is a G-manifold equipped with an invariant bivector
field whose Schouten bracket is the trivector field generated by the invariant
element in $\wedge^3 \g$ associated to an invariant inner product. We introduce
the concept of the fusion for such manifolds, and we relate quasi-Poisson
manifolds to the previously introduced quasi-Hamiltonian manifolds with
group-valued moment maps.
