TY - JOUR
T1 - 2- and 3-variations and finite type invariants of degree 2 and 3
AU - Sakurai, Migiwa
PY - 2013/7/1
Y1 - 2013/7/1
N2 - 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.
AB - 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.
KW - Virtual knot
KW - finite type invariant
KW - local move
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U2 - 10.1142/S0218216513500429
DO - 10.1142/S0218216513500429
M3 - Article
AN - SCOPUS:84880275345
VL - 22
JO - Journal of Knot Theory and its Ramifications
JF - Journal of Knot Theory and its Ramifications
SN - 0218-2165
IS - 8
M1 - 1350042
ER -