Right-angled polyhedra and alternating links

Abhijit Champanerkar, Ilya Kofman, Jessica S. Purcell

Research output: Contribution to journalArticleResearchpeer-review

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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.

Original languageEnglish
Pages (from-to)739-784
Number of pages46
JournalAlgebraic and Geometric Topology
Volume22
Issue number2
DOIs
Publication statusPublished - 2022

Keywords

  • alternating knot
  • Andreev theorem
  • checkerboard surface
  • circle packing
  • Conway sphere
  • guts
  • hyperbolic geometry
  • hyperbolic volume
  • ideal polyhedra
  • right-angled knot
  • right-angled polyhedra
  • weaving knot

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