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A Survey of Hyperbolic Knot Theory

Futer, D
; 
Kalfagianni, E
; 
Purcell, JS
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Pre-print
Date
2019-01-01
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math.GT
 math.GT
 57M25, 57M27, 57M50
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http://hdl.handle.net/20.500.12613/4602
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1708.07201v1.pdf
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DOI
10.1007/978-3-030-16031-9_1
Abstract
© Springer Nature Switzerland AG 2019. 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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Springer International Publishing
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Springer Proceedings in Mathematics and Statistics
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