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The Warping Degree of a Link Diagram by Shimizu, Ayaka is a scholarly article available to read on EtoBox.

What is The Warping Degree of a Link Diagram about?

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)+sr(D) is less than or equal to the crossing number of D, where -D denotes the inverse of D and 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)+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.

Author

Shimizu, Ayaka

Published

2009

Language

EN