For a compact connected nonorientable surface of genus with boundary components, we prove that the natural map from the mapping class group of to the automorphism group of the curve complex of is an isomorphism provided that . We also prove that two curve complexes are isomorphic if and only if the underlying surfaces are diffeomorphic.
Cite this article
Ferihe Atalan, Mustafa Korkmaz, Automorphisms of curve complexes on nonorientable surfaces. Groups Geom. Dyn. 8 (2014), no. 1, pp. 39–68DOI 10.4171/GGD/216