Bounded ideal triangulations of infinite Riemann surfaces
Geometric Topology
2025-02-11 v1 Complex Variables
Abstract
We introduce a notion of a bounded ideal triangulation of an infinite Riemann surface and parametrize Teichm\"uller spaces of infinite surfaces which allow bounded triangulations. We prove that our parametrization is real-analytic. Riemann surfaces with bounded geometry and countably many punctures belong to the class of surfaces with bounded ideal triangulations. In comparison, the Fenchel-Nielsen parametrization for surfaces with bounded geometry is not known, while the Fenchel-Nielsen parametrization for surfaces with bounded pants decompositions is known as a homeomorphism but it is not known whether it is real-analytic
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Cite
@article{arxiv.2502.05590,
title = {Bounded ideal triangulations of infinite Riemann surfaces},
author = {Casey Whitney and Dragomir Saric},
journal= {arXiv preprint arXiv:2502.05590},
year = {2025}
}
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33 pages