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Preprints, Working Papers, ... (Preprint) Year : 2022

Computing a Dirichlet domain for a hyperbolic surface

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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 length and the genus of the surface.
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  • HAL Id : hal-03881015 , version 1

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Vincent Despré, Benedikt Kolbe, Hugo Parlier, Monique Teillaud. Computing a Dirichlet domain for a hyperbolic surface. 2022. ⟨hal-03881015⟩
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