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Quasi-Fuchsian groups and complex realisations of q-deformed real numbers
Abstract
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.
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BibTeX
@misc{elzenaar2026quasifuchsian,
title = {{Quasi-Fuchsian groups and complex realisations of $q$-deformed real numbers}},
author = {Alex Elzenaar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29831},
eprint = {2609.29831},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29831},
}
RIS
TY - UNPB
TI - Quasi-Fuchsian groups and complex realisations of q-deformed real numbers
AU - Alex Elzenaar
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.29831
UR - https://arxiv.org/abs/2609.29831
AB - 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.
ER -