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Up-down colorings of virtual-link diagrams and the necessity of Reidemeister moves of type II.
- Source :
-
Journal of Knot Theory & Its Ramifications . Oct2017, Vol. 26 Issue 12, p-1. 17p. - Publication Year :
- 2017
-
Abstract
- 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 -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 , there exists a diagram representing the same virtual-knot such that any sequence of generalized Reidemeister moves between them includes at least one Reidemeister move of type II. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02182165
- Volume :
- 26
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Journal of Knot Theory & Its Ramifications
- Publication Type :
- Academic Journal
- Accession number :
- 125950120
- Full Text :
- https://doi.org/10.1142/S0218216517500730