2017年10月
Up-down colorings of virtual-link diagrams and the necessity of Reidemeister moves of type II
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
- ,
- ,
- 巻
- 26
- 号
- 12
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1142/S0218216517500730
- 出版者・発行元
- WORLD SCIENTIFIC PUBL CO PTE LTD
We introduce an up-down coloring of a virtual-link (or classical-link) diagram. The colorabilities give a lower bound of the minimum number of Reidemeister moves of type II which are needed between two 2-component virtual-link (or classical-link) diagrams. By using the notion of a quandle cocycle invariant, we give a method to detect the necessity of Reidemeister moves of type II between two given virtual-knot (or classical-knot) diagrams. As an application, we show that for any virtual-knot diagram D, there exists a diagram D ' representing the same virtual-knot such that any sequence of generalized Reidemeister moves between them includes at least one Reidemeister move of type II.
- リンク情報
- ID情報
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- DOI : 10.1142/S0218216517500730
- ISSN : 0218-2165
- eISSN : 1793-6527
- Web of Science ID : WOS:000414219000002