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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 Liftable Homeomorphisms of Cyclic and Rank Two Finite Abelian Branched Covers Over the Real Projective Plane(Elsevier, 2021) Atalan, Ferihe; Medetogullari, Elif; Ozan, YildirayIn this note, we investigate the property for regular branched finite abelian covers of the real projective plane, where each homeomorphism of the base (preserving the branch locus) lifts to a homeomorphism of the covering surface. (C) 2020 Elsevier B.V. All rights reserved.Article Citation - WoS: 3Citation - Scopus: 3Liftable Homeomorphisms of Rank Two Finite Abelian Branched Covers(Springer Basel Ag, 2021) Atalan, Ferihe; Atalan, Ferihe; Medetogullari, Elif; Ozan, Yildiray; Medetoğulları, Elif; Atalan, Ferihe; Medetoğulları, Elif; Mathematics; MathematicsWe investigate branched regular finite abelian A-covers of the 2-sphere, where every homeomorphism of the base (preserving the branch locus) lifts to a homeomorphism of the covering surface. In this study, we prove that if A is a finite abelian p-group of rank k and Sigma -> S-2 is a regular A-covering branched over n points such that every homeomorphism f:S-2 -> S-2 lifts to Sigma, then n = k + 1. We will also give a partial classification of such covers for rank two finite p-groups. In particular, we prove that for a regular branched A-covering pi : Sigma -> S-2, where A = ZprxZpt, 1 <= r <= t , all homeomorphisms f:S-2 -> S-2 lift to those of Sigma if and only if t = r or t = r + 1 and p = 3.
