Automorphisms of curve complexes on nonorientable surfaces

For a compact connected nonorientable surface N of genus g with n boundary components, we prove that the natural map from the mapping class group of N to the automorphism group of the curve complex of N is an isomorphism provided that g C n 5. We also prove that two curve complexes are isomorphic if and only if the underlying surfaces are diffeomorphic. Mathematics Subject Classification (2010). 57M60, 20F38.