8 citations · 37 across the 9 of their papers we have counts for
11 papers
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…
Strong and weak (1, 2) homotopies on knot projections and new invariants
Noboru Ito, Yusuke Takimura
Every second flat Reidemeister move of knot projections can be decomposed into two types thorough an inverse or direct self-tangency modification, respectively called strong or wea…
RII number of knot projections
Noboru Ito, Yusuke Takimura
Every knot projection is simplified to the trivial spherical curve not increasing double points by using deformations of types 1, 2, and 3 which are analogies of Reidemeister moves…
Crosscap number and knot projections
Noboru Ito, Yusuke Takimura
We introduce an unknotting-type number of knot projections that gives an upper bound of the crosscap number of knots. We determine the set of knot projections with the unknotting-t…