Journal of the Korean Mathematical Society (대한수학회지)
- Volume 56 Issue 4
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- Pages.1063-1081
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- 2019
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- 0304-9914(pISSN)
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- 2234-3008(eISSN)
DOI QR Code
ARC SHIFT NUMBER AND REGION ARC SHIFT NUMBER FOR VIRTUAL KNOTS
Gill, Amrendra;Kaur, Kirandeep;Madeti, Prabhakar
- Received : 2018.09.09
- Accepted : 2019.02.07
- Published : 2019.07.01
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