10 results
Search Results
Now showing 1 - 10 of 10
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 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: 1Citation - Scopus: 1Solving an initial boundary value problem on the semiinfinite interval(Tubitak Scientific & Technological Research Council Turkey, 2016) Atalan, Ferihe; Guseinov, Gusein Sh.We explore the sign properties of eigenvalues and the basis properties of eigenvectors for a special quadratic matrix polynomial and use the results obtained to solve the corresponding linear system of differential equations on the half line subject to an initial condition at t = 0 and a condition at t = infinity.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: 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, MustafaWe 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 infinityArticle 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 Connectedness of the Cut System Complex on Nonorientable Surfaces(Univ Kragujevac, Fac Science, 2022) Ali, Fatema; Atalan, FeriheLet N be a compact, connected, nonorientable surface of genus g with n boundary components. In this note, we show that the cut system complex of N is connected for g < 4 and disconnected for g >= 4. We then define a related complex and show that it is connected for g >= 4.Article Citation - WoS: 1Citation - Scopus: 1On a Quadratic Eigenvalue Problem and Its Applications(Springer Basel Ag, 2013) Atalan, Ferihe; Guseinov, Gusein ShWe investigate the eigenvalues and eigenvectors of a special quadratic matrix polynomial and use the results obtained to solve the initial value problem for the corresponding linear system of differential equations.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.
