Cusp volumes of alternating knots

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.

21 pages, 8 figures; v4: revised final version, with corrected constants throughout the paper; to appear in Geometry & Topology

Cited by in corpus (5)

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• The signature and cusp geometry of hyperbolic knots
• Essential twisted surfaces in alternating link complements
• A survey of hyperbolic knot theory
• Cusp Volumes of Alternating Knots on Surfaces