English

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.

Keywords

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

R2 v1 2026-06-23T11:58:04.295Z