Thickness of skeletons of arithmetic hyperbolic orbifolds
Differential Geometry
2021-03-05 v4 Metric Geometry
Abstract
We show that closed arithmetic hyperbolic n-dimensional orbifolds with larger and larger volumes give rise to triangulations of the underlying spaces whose 1-skeletons are harder and harder to embed nicely in Euclidean space. To show this we generalize an inequality of Gromov and Guth to hyperbolic n-orbifolds and find nearly optimal geodesic triangulations of arithmetic hyperbolic n-orbifolds.
Keywords
Cite
@article{arxiv.1811.05280,
title = {Thickness of skeletons of arithmetic hyperbolic orbifolds},
author = {Hannah Alpert and Mikhail Belolipetsky},
journal= {arXiv preprint arXiv:1811.05280},
year = {2021}
}
Comments
15 pages, filled a gap in the proof of Theorem 2, final version, to appear in J. of Topology & Analysis