Cusp volumes of alternating knots

Marc Lackenby, Jessica S Purcell

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Abstract

We show that the cusp volume of a hyperbolic alternating knot can be bounded above and below in terms of the twist number of an alternating diagram of the knot. This leads to diagrammatic estimates on lengths of slopes, and has some applications to Dehn surgery. Another consequence is that there is a universal lower bound on the cusp density of hyperbolic alternating knots.
Original languageEnglish
Pages (from-to)2053–2078
Number of pages26
JournalGeometry and Topology
Volume20
Issue number4
DOIs
Publication statusPublished - 15 Sep 2016

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