  In this paper, we prove that each injective simplicial map of the arc complex
of a compact, connected, orientable surface with nonempty boundary is induced
by a homeomorphism of the surface. We deduce, from this result, that the group
of automorphisms of the arc complex is naturally isomorphic to the extended
mapping class group of the surface, provided the surface is not a disc, an
annulus, a pair of pants, or a torus with one hole. We also show, for each of
these special exceptions, that the group of automorphisms of the arc complex is
naturally isomorphic to the quotient of the extended mapping class group of the
surface by its center.
