arXiv subjects

S. Öykü Yurttaş

Publications and source records attributed to S. Öykü Yurttaş.

7 recordsLinked to original sources

arXiv2026

Quadratic-time computations for pseudo-Anosov mapping classes

We give a quadratic-time algorithm to compute the stretch factor and the invariant measured foliations for a pseudo-Anosov element of the mapping class group. As input, the algorithm accepts a word (in any given finite generating set for the mapping class group) representing a pseudo-Anosov mapping class, and the length of the word is our measure of complexity for the input. The output is a train track and an integer matrix where the stretch factor is the largest real eigenvalue and the unstable foliation is given by the corresponding eigenvector. This is the first algorithm to compute stretch factors and measured foliations that is known to terminate in sub-exponential time.

math.GT↗

arXiv2025

Detecting Free Products in the Mapping Class Group of Punctured Disks via Dynnikov Coordinates

We prove that Dehn twists about opposite curves that define a complete partition on an $n$-punctured disk $D_n$ generate either a free group or a free product of abelian groups. Additionally, we introduce an algorithm based on Dynnikov coordinates to determine whether a given collection of opposite curves forms a complete partition. This algorithm not only verifies completeness but also reveals the exact structure of the free products generated by these Dehn twists, relying solely on the Dynnikov coordinates of the curves as input.

math.GT↗

arXiv2022

Curves on non--orientable surfaces and crosscap transpositions

Let $N_{g,n}$ be an $n$--punctured non--orientable surface of genus $g$ with one boundary component. For $g\geq 2$ one of the generators of the mapping class group of $N_{g,n}$ is a crosscap transposition. We give explicit formulae for the action of crosscap transpositions and their inverses on the set of multicurves in $N_{g,n}$ in terms of generalized Dynnikov coordinates.

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arXiv2018

Applications of the Dynnikov coordinate system on the boundary of Teichmüller space

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.

math.GT↗

arXiv2017

Integral laminations on non-orientable surfaces

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 give an explicit bijection from the set of integral laminations on $N_{k,n}$ to $(\mathbb{Z}^{2(n+k-2)}\times \mathbb{Z}^k)\setminus \left\{0\right\}$.

math.GT↗

arXiv2015

Dynnikov and train track transition matrices of pseudo-Anosov braids

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.

math.DS↗

arXiv2012

Geometric intersection of curves on punctured disks

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.

math.GT↗