Computing a Dirichlet domain for a hyperbolic surface
Computational Geometry
2022-12-06 v1 Differential Geometry
Geometric Topology
Abstract
The goal of this paper is to exhibit and analyze an algorithm that takes a given closed orientable hyperbolic surface and outputs an explicit Dirichlet domain. The input is a fundamental polygon with side pairings. While grounded in topological considerations, the algorithm makes key use of the geometry of the surface. We introduce data structures that reflect this interplay between geometry and topology and show that the algorithm finishes in polynomial time, in terms of the initial perimeter and the genus of the surface.
Cite
@article{arxiv.2212.01934,
title = {Computing a Dirichlet domain for a hyperbolic surface},
author = {Vincent Despré and Benedikt Kolbe and Hugo Parlier and Monique Teillaud},
journal= {arXiv preprint arXiv:2212.01934},
year = {2022}
}
Comments
15 pages, 5 figures