[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j180615

ARC SHIFT NUMBER AND REGION ARC SHIFT NUMBER FOR VIRTUAL KNOTS

Gill, Amrendra (Department of Mathematics Indian Institute of Technology Ropar)
Kaur, Kirandeep (Department of Mathematics Indian Institute of Technology Ropar)
Madeti, Prabhakar (Department of Mathematics Indian Institute of Technology Ropar)

Publication Information

Journal of the Korean Mathematical Society / v.56, no.4, 2019 , pp. 1063-1081 More about this Journal

Abstract

In this paper, we formulate a new local move on virtual knot diagram, called arc shift move. Further, we extend it to another local move called region arc shift defined on a region of a virtual knot diagram. We establish that these arc shift and region arc shift moves are unknotting operations by showing that any virtual knot diagram can be turned into trivial knot using arc shift (region arc shift) moves. Based upon the arc shift move and region arc shift move, we define two virtual knot invariants, arc shift number and region arc shift number respectively.

Keywords

virtual knot; Gauss diagram; forbidden moves;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

1	A. S. Crans, B. Mellor, and S. Ganzell, The forbidden number of a knot, Kyungpook Math. J. 55 (2015), no. 2, 485-506. DOI
2	M. Goussarov, M. Polyak, and O. Viro, Finite-type invariants of classical and virtual knots, Topology 39 (2000), no. 5, 1045-1068. DOI
3	T. Kanenobu, Forbidden moves unknot a virtual knot, J. Knot Theory Ramifications 10 (2001), no. 1, 89-96. DOI
4	L. H. Kauffman, Virtual knot theory, European J. Combin. 20 (1999), no. 7, 663-690. DOI
5	L. H. Kauffman, A self-linking invariant of virtual knots, Fund. Math. 184 (2004), 135-158. DOI
6	S. Nelson, Unknotting virtual knots with Gauss diagram forbidden moves, J. Knot Theory Ramifications 10 (2001), no. 6, 931-935. DOI
7	M. Sakurai, An affne index polynomial invariant and the forbidden move of virtual knots, J. Knot Theory Ramifications 25 (2016), no. 7, 1650040, 13 pp. DOI
8	A. Shimizu, Region crossing change is an unknotting operation, J. Math. Soc. Japan 66 (2014), no. 3, 693-708. DOI
9	H. Murakami and Y. Nakanishi, On a certain move generating link-homology, Math. Ann. 284 (1989), no. 1, 75-89. DOI