Right-angled polyhedra and alternating links
arXiv:1910.13131 · doi:10.2140/agt.2022.22.739
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.
arXiv comment32 pages, 16 figures. V2 includes minor edits and corrections, mainly to exposition, based on referee comments. To appear in Algebr. Geom. Topol
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