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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.
Publication status:
Accepted
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Institute
Role:
Author
Publisher:
Mathematical Sciences Publishers Publisher's website
Journal:
Geometry and Topology Journal website
Publication date:
2015-01-01
EISSN:
1364-0380
ISSN:
1465-3060
URN:
uuid:ae928841-1140-45aa-910a-2263767ef2bf
Source identifiers:
488519
Local pid:
pubs:488519

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