A Survey of Hyperbolic Knot Theory

David Futer, Efstratia Kalfagianni, Jessica S. Purcell

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

Abstract

We survey some tools and techniques for determining geometric properties of a link complement from a link diagram. In particular, we survey the tools used to estimate geometric invariants in terms of basic diagrammatic link invariants. We focus on determining when a link is hyperbolic, estimating its volume, and bounding its cusp shape and cusp area. We give sample applications and state some open questions and conjectures.

Original languageEnglish
Title of host publicationKnots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016
EditorsColin C. Adams, Cameron McA. Gordon, Vaughan F.R. Jones, Louis H. Kauffman, Sofia Lambropoulou, Kenneth C. Millett, Jozef H. Przytycki, Renzo Ricca, Radmila Sazdanovic
Place of PublicationCham Switzerland
PublisherSpringer
Pages1-30
Number of pages30
Volume284
ISBN (Electronic)9783030160319
ISBN (Print)9783030160302
DOIs
Publication statusPublished - 1 Jan 2019
EventInternational Olympic Academy, 2016 - Ancient Olympia, Greece
Duration: 17 Jul 201623 Jul 2016

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume284
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Olympic Academy, 2016
CountryGreece
CityAncient Olympia
Period17/07/1623/07/16

Keywords

  • Cusp shape
  • Dehn filling
  • Hyperbolic knot
  • Hyperbolic link
  • Slope length
  • Volume

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