Right-angled polyhedra and alternating links
Geometric Topology
2022-08-10 v2
Abstract
To any prime alternating link, we associate a collection of hyperbolic right-angled ideal polyhedra by relating geometric, topological and combinatorial methods to decompose the link complement. The sum of the hyperbolic volumes of these polyhedra is a new geometric link invariant, which we call the right-angled volume of the alternating link. We give an explicit procedure to compute the right-angled volume from any alternating link diagram, and prove that it is a new lower bound for the hyperbolic volume of the link.
Cite
@article{arxiv.1910.13131,
title = {Right-angled polyhedra and alternating links},
author = {Abhijit Champanerkar and Ilya Kofman and Jessica S. Purcell},
journal= {arXiv preprint arXiv:1910.13131},
year = {2022}
}
Comments
32 pages, 16 figures. V2 includes minor edits and corrections, mainly to exposition, based on referee comments. To appear in Algebr. Geom. Topol