On a move reducing the genus of a knot diagram

Kenji Daikoku; Keiichi Sakai; Masamichi Takase

doi:10.1512/iumj.2012.61.4666

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arXiv · 1111.3215

On a move reducing the genus of a knot diagram

Kenji Daikoku·Keiichi Sakai·Masamichi Takase

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Abstract

For a knot diagram we introduce an operation which does not increase the genus of the diagram and does not change its representing knot type. We also describe a condition for this operation to certainly decrease the genus. The proof involves the study of a relation between the genus of a virtual knot diagram and the genus of a knotoid diagram, the former of which has been introduced by Stoimenow, Tchernov and Vdovina, and the latter by Turaev recently. Our operation has a simple interpretation in terms of Gauss codes and hence can easily be computer-implemented.

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Kenji Daikoku, Keiichi Sakai, Masamichi Takase. 2012-01-24. On a move reducing the genus of a knot diagram. https://doi.org/10.1512/iumj.2012.61.4666

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