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Article Citation - WoS: 11Citation - Scopus: 11Automorphisms 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: 4Citation - Scopus: 4Outer Automorphisms of Mapping Class Groups of Nonorientable Surfaces(World Scientific Publ Co Pte Ltd, 2010) Atalan, FeriheLet N(g) be the connected closed nonorientable surface of genus g >= 5 and Mod(Ng) denote the mapping class group of N(g). We prove that the outer automorphism group of Mod(N(g)) is cyclic.Article A Note on Chains and Bounding Pairs of Dehn Twists(Cambridge Univ Press, 2021) Atalan, FeriheLet N-g(k) be a nonorientable surface of genus g with k punctures. In the first part of this note, after introducing preliminary materials, we will give criteria for a chain of Dehn twists to bound a disc. Then, we will show that automorphisms of the mapping class groups map disc bounding chains of Dehn twists to such chains. In the second part of the note, we will introduce bounding pairs of Dehn twists and give an algebraic characterization for such pairs.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.
