Abstract
Goussarov, Polyak and Viro defined a finite type invariant and a local move called an n-variation for virtual knots. In this paper, we give the differences of the values of the finite type invariants of degree 2 and 3 between two virtual knots which can be transformed into each other by a 2- and 3-variation, respectively. As a result, we obtain lower bounds of the distance between long virtual knots by 2-variations and the distance between virtual knots by 3-variations by using the values of the finite type invariants of degree 2 and 3, respectively.
Original language | English |
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Article number | 1350042 |
Journal | Journal of Knot Theory and its Ramifications |
Volume | 22 |
Issue number | 8 |
DOIs | |
Publication status | Published - 2013 Jul 1 |
Externally published | Yes |
Keywords
- Virtual knot
- finite type invariant
- local move
ASJC Scopus subject areas
- Algebra and Number Theory