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Article Citation - WoS: 5Citation - Scopus: 5Automorphisms of the mapping class group of a nonorientable surface(Springer, 2017) Atalan, Ferihe; Szepietowski, BlazejLet S be a nonorientable surface of genus g >= 5 with n >= 0 punctures, and Mod(S) its mapping class group. We define the complexity of S to be the maximum rank of a free abelian subgroup of Mod(S). Suppose that S-1 and S-2 are two such surfaces of the same complexity. We prove that every isomorphism Mod(S-1) -> Mod(S-2) is induced by a diffeomorphism S-1 -> S-2. This is an analogue of Ivanov's theorem on automorphisms of the mapping class groups of an orientable surface, and also an extension and improvement of the first author's previous result.Article Citation - WoS: 12Citation - Scopus: 12Automorphisms of Curve Complexes on Nonorientable Surfaces(European Mathematical Soc, 2014) Atalan, Ferihe; Korkmaz, MustafaFor 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 + n >= 5. We also prove that two curve complexes are isomorphic if and only if the underlying surfaces are diffeomorphic.Article Citation - WoS: 5Citation - Scopus: 4Number of Pseudo-Anosov Elements in the Mapping Class Group of a Four-Holed Sphere(Tubitak Scientific & Technological Research Council Turkey, 2010) Atalan, Ferihe; Korkmaz, Mustafa; Ozan, Ferihe AtalanWe compute the growth series and the growth functions of reducible and pseudo-Anosov elements of the pure mapping class group of the sphere with four holes with respect to a certain generating set We prove that the ratio of the number of pseudo-Anosov elements to that of all elements in a ball with center at the identity tends to one as the radius of the ball tends to infinity
