8 citations · 79 across the 49 of their papers we have counts for
23 papers · 1 filter
Jones polynomials of long virtual knots
Noboru Ito
This paper defines versions of the Jones polynomial and Khovanov homology by using several maps from the set of Gauss diagrams to its variant. Through calculation of some examples,…
Space of chord diagrams on spherical curves
Noboru Ito
In this paper, we give a definition of -valued functions from the ambient isotopy classes of spherical/plane curves derived from chord diagrams, denoted by $\sum_i α_i…
Thirty-two equivalence relations on knot projections
Noboru Ito, Yusuke Takimura
We consider 32 homotopy classifications of knot projections (images of generic immersions from a circle into a 2-sphere). These 32 equivalence relations are obtained based on which…
Strong and weak (1, 3) homotopies on knot Projections
Noboru Ito, Yusuke Takimura, Kouki Taniyama
Strong and weak (1, 3) homotopies are equivalence relations on knot projections, defined by the first flat Reidemeister move and each of two different types of the third flat Reide…
On a nontrivial knot projection under (1, 3) homotopy
Noboru Ito, Yusuke Takimura
In 2001, Östlund formulated the question: are Reidemeister moves of types 1 and 3 sufficient to describe a homotopy from any generic immersion of a circle in a two-dimensional plan…
Circle arrangements of link projections
Noboru Ito, Shosaku Matsuzaki, Kouki Taniyama
An oriented link projection is the image of a generic immersion of oriented circles into the 2-sphere. The circle arrangement of a link projection is a disjoint union of unoriented…