# Cusp volumes of alternating knots

@inproceedings{Lackenby2016CuspVO, title={Cusp volumes of alternating knots}, author={Marc Lackenby and Jessica S. Purcell}, year={2016} }

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.

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#### Citations

##### Publications citing this paper.

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## State Surfaces of Links

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CITES BACKGROUND

## Geometry of alternating links on surfaces.

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## Waist size for cusps in hyperbolic 3-manifolds II

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## A survey of hyperbolic knot theory

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CITES BACKGROUND

## Only finitely many alternating knots can yield a given manifold by surgery

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CITES METHODS & BACKGROUND

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