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GAPS BETWEEN CONSECUTIVE UNTWISTING NUMBERS
Published online by Cambridge University Press: 03 February 2020
Abstract
For p ≥ 1, one can define a generalisation of the unknotting number tup called the pth untwisting number, which counts the number of null-homologous twists on at most 2p strands required to convert the knot to the unknot. We show that for any p ≥ 2 the difference between the consecutive untwisting numbers tup–1 and tup can be arbitrarily large. We also show that torus knots exhibit arbitrarily large gaps between tu1 and tu2.
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- Research Article
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- © The Author(s) 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust
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