Two-sided combinatorial volume bounds for non-obtuse hyperbolic polyhedra
Geometric Topology
2012-11-22 v1
Abstract
We give a method for computing upper and lower bounds for the volume of a non-obtuse hyperbolic polyhedron in terms of the combinatorics of the 1-skeleton. We introduce an algorithm that detects the geometric decomposition of good 3-orbifolds with planar singular locus and underlying manifold the 3-sphere. The volume bounds follow from techniques related to the proof of Thurston's Orbifold Theorem, Schl\"afli's formula, and previous results of the author giving volume bounds for right-angled hyperbolic polyhedra.
Cite
@article{arxiv.1008.5396,
title = {Two-sided combinatorial volume bounds for non-obtuse hyperbolic polyhedra},
author = {Christopher K. Atkinson},
journal= {arXiv preprint arXiv:1008.5396},
year = {2012}
}
Comments
36 pages, 19 figures