ON THE Cn-DISTANCE AND VASSILIEV INVARIANTS
2012 ◽
Vol 21
(10)
◽
pp. 1250097
◽
A local move called a Cn-move is closely related to Vassiliev invariants. A Cn-distance between two knots K and L, denoted by dCn(K, L), is the minimum number of times of Cn-moves needed to transform K into L. Let p and q be natural numbers with p > q ≥ 1. In this paper, we show that for any pair of knots K1 and K2 with dCn(K1, K2) = p and for any given natural number m, there exist infinitely many knots Jj(j = 1, 2, …) such that dCn(K1, Jj) = q and dCn(Jj, K2) = p - q, and they have the same Vassiliev invariants of order less than or equal to m. In the case of n = 1 or 2, the knots Jj(j = 1, 2, …) satisfy more conditions.
2001 ◽
Vol 10
(07)
◽
pp. 1041-1046
◽
Keyword(s):
2018 ◽
Keyword(s):
2002 ◽
Vol 133
(2)
◽
pp. 325-343
◽
2012 ◽
Vol 22
(4-5)
◽
pp. 614-704
◽
2013 ◽
Vol 13
(4-5)
◽
pp. 847-861
◽
Keyword(s):
2011 ◽
Vol 07
(03)
◽
pp. 579-591
◽
Keyword(s):
1996 ◽
Vol 48
(3)
◽
pp. 512-526
◽
1967 ◽
Vol 63
(2)
◽
pp. 389-392
◽