2- AND 3-VARIATIONS AND FINITE TYPE INVARIANTS OF DEGREE 2 AND 3
2013 ◽
Vol 22
(08)
◽
pp. 1350042
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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.
2013 ◽
Vol 22
(06)
◽
pp. 1350024
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Keyword(s):
2012 ◽
Vol 21
(13)
◽
pp. 1240001
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Keyword(s):
2004 ◽
Vol 13
(01)
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pp. 1-11
2019 ◽
Vol 28
(10)
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pp. 1950064
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2006 ◽
Vol 15
(09)
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pp. 1163-1199
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2007 ◽
Vol 142
(3)
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pp. 459-468
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2008 ◽
Vol 19
(06)
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pp. 747-766
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2000 ◽
Vol 09
(06)
◽
pp. 735-758
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Keyword(s):