Journal of Knot Theory and Its Ramifications 28(12) 1950074-1950074 Oct 2019 [Refereed]
Satoh and Taniguchi introduced the [Formula: see text]-writhe [Formula: see text] for each non-zero integer [Formula: see text], which is an invariant for virtual knots. The [Formula: see text]-writhes give the coefficients of some polynomial inva...
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 26(13) Nov 2017 [Refereed]
We consider a local move, denoted by., on knot diagrams or virtual knot diagrams. If two (virtual) 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 numbe...
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 23(4) Apr 2014 [Refereed]
A local move called a C-n-move is closely related to Vassiliev invariants. The C-n-distance between two knots K and L, denoted by d(Cn) (K, L), is the minimal number of C-n-moves needed to transform K into L. In the case of n >= 3, we show that...
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 19(4) 503-507 Apr 2010
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 Apr 2010
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...
HIROSHIMA MATHEMATICAL JOURNAL 39(3) 443-450 Nov 2009
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 Jul 2008
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...
Topology of knots and 3-manifoldsJapan Society for the Promotion of Science: Grants-in-Aid for Scientific ResearchOhtsuki Tomotada KAMADA Seiichi HABIRO Kazuo
Project Year: Apr 2012 - Mar 2017
Studies of knot theory and their applicationsJapan Society for the Promotion of Science: Grants-in-Aid for Scientific ResearchKAWAUCHI Akio KAMADA Seiichi SAKUMA Makoto NAKANISHI Yasutaka TANIYAMA Kouki OOYAMA Toshiyuki MOTEGI Kimihiko GOUDA Hiroshi SHIMOKAWA Koya TERAGAITO Masakazu SATOU Shin TANAKA Toshihumi IWAKIRI Masahide CHON Inde KISHIMOTO Kengo OTSUKI Tomotada SHIMIZU Ayaka
School of Arts and Sciences
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