A survey of hyperbolic knot theory

David Futer; Efstratia Kalfagianni; Jessica S. Purcell

doi:10.1007/978-3-030-16031-9_1

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arXiv · 1708.07201

A survey of hyperbolic knot theory

David Futer·Efstratia Kalfagianni·Jessica S. Purcell

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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.

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David Futer, Efstratia Kalfagianni, Jessica S. Purcell. 2017-08-23. A survey of hyperbolic knot theory. https://doi.org/10.1007/978-3-030-16031-9_1

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