Injective Simplicial Maps of the Arc Complex on Nonorientable Surfaces

摘要

We prove that each injective simplicial map from the arc complex of acompact, connected, nonorientable surface with nonempty boundary to itself isinduced by a homeomorphism of the surface. We also prove that the automorphismgroup of the arc complex is isomorphic to the quotient of the mapping classgroup of the surface by its center.