发表机构
Monash University（蒙纳士大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文将$q$-有理数与$q$-实数理论联系到Kleinian群和Teichmüller空间，提供几何视角，并解决了关于$q$-变形Farey镶嵌拓扑的猜想。
AI 中文摘要
我们将Morier-Genoud和Ovsienko引入的$q$-有理数和$q$-实数理论联系到Kleinian群及其Teichmüller空间的经典理论。这为关于$q \in \mathbb{C}$特定值下$q$-有理数实现的若干近期结果提供了几何视角。作为应用，我们解决了Bapat、Becker和Licata关于$q$-变形Farey镶嵌拓扑的一个猜想。
英文摘要
We relate the theory of $q$-rational and $q$-real numbers introduced by Morier-Genoud and Ovsienko to the classical theory of Kleinian groups and their Teichmüller spaces. This provides a geometric point of view on several recent results about realisations of $q$-rationals for particular values of $ q \in \mathbb{C} $. As an application we resolve a conjecture of Bapat, Becker, and Licata on the topology of the $q$-deformed Farey tessellation.
Comments15 pages, 6 figures. Comments are welcome. v2: fix mistakes in treatment of r/s<0 (basically minor definitional errors, no substantial changes to statements or proofs)
