  We prove that Manolescu and Woodward's Symplectic Instanton homology, and its
twisted versions are natural, and define maps associated to four dimensional
cobordisms within this theory.
  This allows one to define representations of the mapping class group and the
fundamental group of a 3-manifold, and to have a geometric interpretation of
the maps appearing in the long exact sequence for symplectic instanton
homology, together with vanishing criterions.
