Doç. Dr. S.Öykü Yurttaş

Dicle Üniversitesi, Fen Fakültesi Matematik Bölümü 21280, 

Diyarbakır, Türkiye

(+90) 412-2488666- (3004) 

saadet (dot) yurttas (at) dicle (dot) edu (dot) tr

Araştırma Alanları: Düşük boyutlu topoloji, gönderim sınıfları grubu, topolojik dinamik sistemler, hesaplamalı topoloji: Dynnikov koordinatları, train track koordinatları ve Dehn-Thurston koordinatları gibi global koordinatlar yardımıyla yüzey homeomorfizmaları ile ilgili dinamiksel problemler ve çoklu eğriler ile ilgili kombinatorik problemlere algoritmik yaklaşımlar CV

           Makaleler:

A method for computing the topological entropy of each braid in an infinite family, making use of Dynnikov's coordinates on the boundary of Teichmüller space, is described. The method is illustrated on two two-parameter families of braids.


We give a recipe to compute the geometric intersection number of an integral lamination with a particular type of integral lamination on an n-times punctured disk. This provides a way to find the geometric intersection number of two arbitrary integral laminations when combined with an algorithm of Dynnikov and Wiest.


We compare the spectra of Dynnikov matrices with the spectra of the train track transition matrices of a given pseudo-Anosov braid on the finitely punctured disk, and show that these matrices are isospectral up to roots of unity and zeros under some particular conditions. It is shown, via examples, that Dynnikov matrices are much easier to compute than transition matrices, and so yield data that was previously inaccessible.


We present an efficient algorithm for calculating the number of components of an integral lamination on an n-punctured disk given its Dynnikov coordinates. The algorithm requires O(n^2M) arithmetic operations where M is the sum of the absolute values of the Dynnikov coordinates.


         

We describe triangle coordinates for integral laminations on a non-orientable surface N_{k,n} of genus k with n punctures and one boundary component, and we give an explicit bijection from the set of integral laminations on N_{k,n} to (Z^2(n+k−2) × Z^k )\ {0}.


We present an algorithm for calculating the geometric intersection number of two multicurves on the n-punctured disk, taking as input their Dynnikov coordinates. The algorithm has complexity O(m^2n^4 ), where m is the sum of the absolute values of the Dynnikov coordinates of the two multicurves. The main ingredient is an algorithm due to Cumplido for relaxing a multicurve.


The Dynnikov coordinate system puts global coordinates on the boundary of Teichmüller space of an n–punctured disk. We survey the Dynnikov coordinate system, and investigate how we use this coordinate system to study pseudo– Anosov braids making use of results from Thurston’s theory on surface homeomorphisms.


Let N_{g,n} denote a non–orientable 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 N_{g,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.


A short survey on  computing the dilatation and invariant measured foliations of each member of a simple family of pseudo-Anosov braids is given. 

     




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