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On the Semi-threading of Knot Diagrams with Minimal Overpasses by Chung, Jae-Wook; Jeong, Seulgi; Kim, Dongseok is a scholarly article available to read on EtoBox.

What is On the Semi-threading of Knot Diagrams with Minimal Overpasses about?

Given a knot diagram $D$, we construct a semi-threading circle for it which can be an axis of $D$ as a closed braid depending on knot diagrams. In particular, we consider semi-threading circles for minimal diagrams of a knot with respect to overpasses which give us some information related to the braid index. By this notion, we show that, for every nontrivial knot $K$, the braid index $b(K)$ of $K$ is not less than the minimum number $l(K)$ of overpasses of diagrams. Moreover, they are the same for a torus knot.

Author

Chung, Jae-Wook; Jeong, Seulgi; Kim, Dongseok

Published

2013

Language

EN