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GAPS BETWEEN CONSECUTIVE UNTWISTING NUMBERS

Part of: Low-dimensional topology

Published online by Cambridge University Press:  03 February 2020

DUNCAN MCCOY
DUNCAN MCCOY*
Affiliation:
Département de mathématiques, Université du Québec à Montréal, Montréal QC H3C3P8, Canada e-mail: duncan.mccoy@cirget.ca
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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.

MSC classification

Primary: 57M25: Knots and links in $S^3$
Secondary: 57M27: Invariants of knots and 3-manifolds
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 63 , Issue 1 , January 2021 , pp. 59 - 65
Copyright
© The Author(s) 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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References

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