Journal of Knot Theory and its Ramifications 22(9) 2013年8月 [査読有り]
Hirasawa and Uchida defined the Gordian complex of knots which is a simplicial complex whose vertices consist of all knot types in S3. In this paper, we define the Gordian complex of virtual knots by using forbidden moves. We show that for any vir...
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY 155(1) 39-46 2013年7月 [査読有り]
We consider a local move on a knot diagram, where we denote the local move by lambda. If two knots K-1 and K-2 are transformed into each other by a finite sequence of lambda-moves, the lambda-distance between K-1 and K-2 is the minimum number of t...
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 21(14) 2012年12月 [査読有り]
Hirasawa and Uchida defined the Gordian complex of knots which is a simplicial complex whose vertices consist of all knot types in S-3. In this paper, we define the Gordian complex of virtual knots which is a simplicial complex whose vertices cons...
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 21(10) 2012年9月 [査読有り]
A local move called a C-n-move is closely related to Vassiliev invariants. A C-n-distance between two knots K and L, denoted by d(Cn) (K, L), is the minimum number of times of C-n-moves needed to transform K into L. Let p and q be natural numbers ...
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 19(9) 1125-1134 2010年9月 [査読有り]
We define an invariant for two component spatial graphs. Although the definition of the invariant is alike a linking number, it is different from the absolute value of a linking number. We show that the invariant is not a finite type invariant.
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 19(4) 503-507 2010年4月
Adams et al. introduce the notion of almost alternating links; non-alternating links which have a projection whose one crossing change yields an alternating projection. For an alternating knot K, we consider the number Alm(K) of almost alternating...
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 19(4) 503-507 2010年4月
Adams et al. introduce the notion of almost alternating links; non-alternating links which have a projection whose one crossing change yields an alternating projection. For an alternating knot K, we consider the number Alm(K) of almost alternating...
After the works of Kauffman-Banchoff and Yamasaki, it is known that a local move called the pass move is strongly related to the Arf invariant, which is equivalent to the parity of the coefficient of the degree two term in the Conway polynomial. O...
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 17(7) 771-785 2008年7月
It is shown that two knots can be transformed into each other by C-n-moves if and only if they have the same Vassiliev invariants of order less than n. Consequently, a C-n-move cannot change the Vassiliev invariants of order less than n and may ch...
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