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March 2011 The warping degree of a link diagram
Ayaka Shimizu
Osaka J. Math. 48(1): 209-231 (March 2011).


For an oriented link diagram $D$, the warping degree $d(D)$ is the smallest number of crossing changes which are needed to obtain a monotone diagram from $D$. We show that $d(D) + d(-D) + \mathit{sr}(D)$ is less than or equal to the crossing number of $D$, where $-D$ denotes the inverse of $D$ and $\mathit{sr}(D)$ denotes the number of components which have at least one self-crossing. Moreover, we give a necessary and sufficient condition for the equality. We also consider the minimal $d(D) + d(-D) + \mathit{sr}(D)$ for all diagrams $D$. For the warping degree and linking warping degree, we show some relations to the linking number, unknotting number, and the splitting number.


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Ayaka Shimizu. "The warping degree of a link diagram." Osaka J. Math. 48 (1) 209 - 231, March 2011.


Published: March 2011
First available in Project Euclid: 22 March 2011

zbMATH: 1248.57007
MathSciNet: MR2802599

Primary: 57M25
Secondary: 57M27

Rights: Copyright © 2011 Osaka University and Osaka City University, Departments of Mathematics


Vol.48 • No. 1 • March 2011
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