Zobrazeno 1 - 10
of 67
pro vyhledávání: '"Takimura, Yusuke"'
Autor:
Ito, Noboru, Takimura, Yusuke
Publikováno v:
Topology Proc. 60 (2022), 31--44
A generic immersion of a circle into a $2$-sphere is often studied as a projection of a knot; it is called a knot projection. A chord diagram is a configuration of paired points on a circle; traditionally, the two points of each pair are connected by
Externí odkaz:
http://arxiv.org/abs/2108.10133
Autor:
Ito, Noboru, Takimura, Yusuke
Publikováno v:
Topology Proc. 53 (2019), 177--199
This paper provides the complete table of prime knot projections with their mirror images, without redundancy, up to eight double points systematically thorough a finite procedure by flypes. In this paper, we show how to tabulate the knot projections
Externí odkaz:
http://arxiv.org/abs/2108.09698
Autor:
Ito, Noboru, Takimura, Yusuke
Publikováno v:
Topology Appl. 225 (2017), 130--138
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 moves are forbidden among the five type of Reidemeister moves. We sho
Externí odkaz:
http://arxiv.org/abs/2012.02612
Publikováno v:
Osaka J. Math. 52 (2015), no. 3, 617--646
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 Reidemeister moves. In this paper, we introduce the cross chord number that
Externí odkaz:
http://arxiv.org/abs/2012.00303
Autor:
Ito, Noboru, Takimura, Yusuke
Publikováno v:
Topology Appl. 210 (2016), 22--28
In 2001, \"Ostlund 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 plane to an embedding of the circle? The positive answer to this questio
Externí odkaz:
http://arxiv.org/abs/2011.14322
Autor:
Ito, Noboru, Takimura, Yusuke
Publikováno v:
Kobe J. Math. 33 (2016), 13--30
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 weak, when orientations of the knot projections are arbitrarily provided.
Externí odkaz:
http://arxiv.org/abs/2011.07228
Autor:
Ito, Noboru, Takimura, Yusuke
Publikováno v:
Kobe J. Math. 37 (2020)
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 of types 1, 2, and 3 on knot diagrams. We introduce RII number of a k
Externí odkaz:
http://arxiv.org/abs/2010.10793
Autor:
Ito, Noboru, Takimura, Yusuke
Publikováno v:
Internat. J. Math. Vol. 29, No. 12, 1850084 (2018)
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-type number at most two, and this result implies classical and new resu
Externí odkaz:
http://arxiv.org/abs/2008.11061
Autor:
Ito, Noboru, Takimura, Yusuke
Publikováno v:
Topology Appl. 193 (2015), 290--301
Reductivity of knot projections refers to the minimum number of splices of double points needed to obtain reducible knot projections. Considering the type and method of splicing (Seifert type splice or non-Seifert type splice, recursively or simultan
Externí odkaz:
http://arxiv.org/abs/2006.10257
Autor:
Ito, Noboru, Takimura, Yusuke
Publikováno v:
Triple chords and strong (1, 2) homotopy, J. Math. Soc. Japan 68 (2016). 637--651
A triple chord is a sub-diagram of a chord diagram that consists of a circle and finitely many chords connecting the preimages for every double point on a spherical curve, and it has exactly three chords giving the triple intersection. This paper des
Externí odkaz:
http://arxiv.org/abs/2005.10551