Atalan, Ferihe
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Name Variants
Ozan, Ferihe Atalan
Ferihe Atalan
Atalan,F.
Atalan,Ferihe
Ferihe, Atalan
A., Ferihe
A.,Ferihe
Atalan, Ferihe
F.,Atalan
Atalan F.
F., Atalan
Ferihe Atalan
Atalan,F.
Atalan,Ferihe
Ferihe, Atalan
A., Ferihe
A.,Ferihe
Atalan, Ferihe
F.,Atalan
Atalan F.
F., Atalan
Job Title
Profesör Doktor
Email Address
ferihe.atalan@atilim.edu.tr
ORCID ID
Scopus Author ID
Turkish CoHE Profile ID
Google Scholar ID
WoS Researcher ID
Scholarly Output
15
Articles
12
Citation Count
27
Supervised Theses
3
15 results
Scholarly Output Search Results
Now showing 1 - 10 of 15
Master Thesis Bir yüzey üzerindeki Hatcher-Thurston kompleksi(2016) Atalan, Ferihe; Ozan, Ferihe Atalan; MathematicsBu tezde, kompakt, bağlantılı, yönlendirilebilen cins sayısı $g \geq 1$ olan bir yüzey için E. Irmak ve M. Korkmaz'ın Hatcher-Thurston kompleksinin otomorfizma grubu üzerindeki çalışmalarını inceleyeceğiz. Daha açık olarak, bu otomorfizma grubunun yönlendirilebilen yüzeyin genişletilmiş gönderim sınıf grubunun merkezine bölümüne izomorfik olduğu gerçeği üzerinde çalışılmaktadır. Bu tezin son bölümünde, cins sayısı $g \geq 1$ olan kompakt, bağlantılı, yönlendirilemeyen yüzeyler için Hatcher-Thurston kompleksini ve kesme sistemlerini tanımlayacağız.Article Citation Count: 0A NOTE ON CHAINS AND BOUNDING PAIRS OF DEHN TWISTS(Cambridge Univ Press, 2021) Atalan, Ferihe; MathematicsLet 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.Master Thesis Eğri grafının otomorfizmaları(2017) Atalan, Ferihe; Ozan, Ferihe Atalan; MathematicsBu tezde, yüzeyler üzerindeki ayırmayan eğrilerin belli bir grafının otomorfizmalarını ve iki-taraflı eğrilerin komplekslerinin otomorfizmalarını çalışacağız. Üçüncü bölümde, cins sayısı g >= 1 ve n delikli yönlendirilebilen yüzeyler için P. S. Schaller'ın hiperbolik yüzeylerin gönderim sınıf grupları ve grafların otomorfizma grupları üzerine yaptığı çalışmasını ele alacağız. Daha açık olarak, Schaller tarafından ispat edilen belli bir grafın otomorfizma grubunun yönlendirilebilen yüzeyin genişletilmiş gönderim sınıf grubuna izomorfik olduğu gösterilmektedir. Bu tezin son bölümünde, cins sayısı g ve n delikli yönlendirilemeyen yüzeyler üzerindeki iki-taraflı basit kapalı eğrilerin komplekslerinin otomorfizmalarını çalışacağız.Article Citation Count: 3Liftable homeomorphisms of rank two finite abelian branched covers(Springer Basel Ag, 2021) Atalan, Ferihe; Medetogullari, Elif; Medetoğulları, Elif; 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.Article Citation Count: 0CONNECTEDNESS OF THE CUT SYSTEM COMPLEX ON NONORIENTABLE SURFACES(Univ Kragujevac, Fac Science, 2022) Atalan, Ferihe; Atalan, Ferihe; MathematicsLet 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 Count: 1On a Quadratic Eigenvalue Problem and its Applications(Springer Basel Ag, 2013) Atalan, Ferihe; Guseinov, Gusein Sh; Hüseyin, Hüseyin Şirin; MathematicsWe 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 Count: 5Number 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; MathematicsWe 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 Citation Count: 5Automorphisms of the mapping class group of a nonorientable surface(Springer, 2017) Atalan, Ferihe; Szepietowski, Blazej; MathematicsLet 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 Count: 9Automorphisms of curve complexes on nonorientable surfaces(European Mathematical Soc, 2014) Atalan, Ferihe; Korkmaz, Mustafa; MathematicsFor 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 Count: 0MOVES ON CURVES ON NONORIENTABLE SURFACES(Rocky Mountain Mathematics Consortium, 2022) Atalan, Ferihe; Yurttaş,S.Ö.; MathematicsLet 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 L with so-called relaxed curves in Ng,n making use of measured π1-train tracks. The algorithm proceeds by the repeated application of three moves which take as input the measures of L and produces as output a multicurve L′ which is minimal with respect to each of the relaxed curves. The last step of the algorithm calculates the number of intersections between L′ and the relaxed curves. © Rocky Mountain Mathematics Consortium.
