3 papers
math.CO2025
Equivariant Modular Functions and Quantizations of Continued Fractions
Mustafa Topkara, A. Muhammed Uludag
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 grou…
math.GT2018
Mapping class groupoids and Thompson's groups
A. Muhammed Uludağ, Mustafa Topkara, Özge Ülkem +1
We introduce a groupoid ${\mathbf{ΠMG}}}$, called the fundamental modular groupoid, which is a variant of Penner's mapping class groupoid. We study how it relates to the surface ma…
math.AT2016
Monodromy of torus fiber bundles and decomposability problem
Mahir Bilen Can, Mustafa Topkara
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…