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Article Moves on Curves on Nonorientable Surfaces(Rocky Mt Math Consortium, 2022) Atalan, Ferihe; Yurttas, S. OykuLet Ng,n denote a nonorientable surface of genus g with n punctures and one boundary component. We give an algorithm to calculate the geometric intersection number of an arbitrary multicurve d. with so-called relaxed curves in Ng,n making use of measured n1-train tracks. The algorithm proceeds by the repeated application of three moves which take as input the measures of d. and produces as output a multicurve d.' which is minimal with respect to each of the relaxed curves. The last step of the algorithm calculates the number of intersections between d.' and the relaxed curves.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: 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 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.
