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Geometric estimates from spanning surfaces
Author(s) -
Burton Stephan D.,
Kalfagianni Efstratia
Publication year - 2017
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12063
Subject(s) - mathematics , meridian (astronomy) , knot (papermaking) , bounded function , embedding , knot theory , diagrammatic reasoning , combinatorics , geometry , mathematical analysis , computer science , physics , astronomy , chemical engineering , artificial intelligence , engineering , programming language
We derive bounds on the length of the meridian and the cusp volume of hyperbolic knots in terms of the topology of essential surfaces spanned by the knot. We provide an algorithmically checkable criterion that guarantees that the meridian length of a hyperbolic knot is below a given bound. As applications we find knot diagrammatic upper bounds on the meridian length and the cusp volume of hyperbolic adequate knots and we obtain new large families of knots with meridian lengths bounded above by four. We also discuss applications of our results to Dehn surgery.