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 |
|---|---|
| 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
- finite type invariant
- local move
- Virtual knot
ASJC Scopus subject areas
- Algebra and Number Theory
Cite this
2- and 3-variations and finite type invariants of degree 2 and 3. / Katou, Migiwa.
In: Journal of Knot Theory and its Ramifications, Vol. 22, No. 8, 1350042, 01.07.2013.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - 2- and 3-variations and finite type invariants of degree 2 and 3
AU - Katou, 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 - finite type invariant
KW - local move
KW - Virtual knot
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UR - http://www.scopus.com/inward/citedby.url?scp=84880275345&partnerID=8YFLogxK
U2 - 10.1142/S0218216513500429
DO - 10.1142/S0218216513500429
M3 - Article
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 -