arXiv subjects

Mustafa Topkara

Publications and source records attributed to Mustafa Topkara.

3 recordsLinked to original sources

arXiv2025

Equivariant Modular Functions and Quantizations of Continued Fractions

We show that, in addition to the quantizations of the rational numbers discovered by Morier-Genoud and Ovsienko, there exist a pair of conjugate representations of the modular group and the corresponding equivariant maps with respect to these representations. We discuss some specializations of these quantizations and discuss its connection to Dyer's outer automorphism and the associated involution Jimm of the real line.

math.CO↗

arXiv2018

Mapping class groupoids and Thompson's groups

We introduce a groupoid ${\mathbf{\Pi MG}}}$, called the fundamental modular groupoid, which is a variant of Penner's mapping class groupoid. We study how it relates to the surface mapping class groups and Thompson's group $\mathsf T$. We also introduce larger groupoid $\mathbf{\Omega MG}$, which is related to outer automorphisms of free groups and Thompson's group $\mathsf V$ in a similar manner.

math.GT↗

arXiv2017

Monodromy of torus fiber bundles and decomposability problem

The notion of a (stably) decomposable fiber bundle is introduced. In low dimensions, for torus fiber bundles over a circle the notion translates into a property of elements of the special linear group of integral matrices. We give a complete characterization of the stably decomposable torus fiber bundle of fiber-dimension less than 4 over the circle.

math.AT↗