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Right-angled polyhedra
and alternating links
Abhijit Champanerkar, Ilya Kofman and Jessica S Purcell |
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Algebraic & Geometric Topology 22 (2022) 739–784
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Abstract |
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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. |
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Keywords
hyperbolic geometry, alternating knot, guts, circle
packing, right-angled polyhedra, ideal polyhedra,
checkerboard surface, Conway sphere, Andreev theorem,
hyperbolic volume, weaving knot, right-angled knot
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Mathematical Subject Classification 2010
Primary: 57M25, 57M27, 57M50
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References |
Publication
Received: 20 February 2020
Revised: 22 January 2021
Accepted: 22 February 2021
Published: 3 August 2022
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Authors |
| Abhijit Champanerkar | |
| Department of Mathematics College of Staten Island City University of New York Staten Island, NY United States |
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| Ilya Kofman | |
| Department of Mathematics College of Staten Island City University of New York New York, NY United States |
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| Jessica S Purcell | |
| School of Mathematics Monash University Clayton VIC Australia |
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