We consider the cosmetic surgery problem for two-bridge knots in the 3-sphere. We first verify by using previously known results that all the two-bridge knots of at most 9 crossings admit no purely cosmetic surgery pairs except for the knot 9_27. ...
We consider a random link, which is defined as the closure of a braid obtained from a random walk on the braid group. For such a random link, the expected value for the number of components was calculated by Jiming Ma. In this paper, we determine ...
Journal of Knot Theory and Its Ramifications 26 1750018-1-1750018-23 2017年2月 [査読有り]
For a link with zero determinants, a ℤ-coloring is defined as a generalization of Fox coloring. We call a link having a diagram which admits a non-trivial ℤ-coloring a ℤ-colorable link. The minimal coloring number of a ℤ-colorable link is the mini...
A lower bound on minimal number of colors for links
市原一裕，松土恵理
Kobe Journal of Mathematics 33(1-2) 53-60 2016年12月 [査読有り]
We show that the minimal number of colors for all effective n-colorings of a link with non-zero determinant is at least 1+log_2 n.
研究集会 Intelligence of Low-dimensional Topology 2018年5月30日
One of the most well-known invariants of knots and links would be the Fox n-coloring for an integer n. On the other hand, there exist certain links known to admit a non- trivial n-coloring for any integer n. For such a link, one can define a Z-col...
I will report on our recent study of chirally cosmetic surgery, that is, a pair of Dehn surgeries on a knot producing homeomorphic 3-manifolds with opposite orientations. Several constraints on knots and surgery slopes to admit such surgeries are ...
OIST Mini Symposium "Computational Problems in Low-dimensional Topology" 2018年3月14日 沖縄科学技術大学院大学
I will give a survey of my results on exceptional Dehn surgeries on knots and links.It will includes classification theorems of exceptional surgeries on alternating knots, on Montesinos knots, and on 2-bridge links.Part of contents are based on jo...
I report our recent results about vanishing of nontrivial elements in the fundamental group of an orientable 1-cusped hyperbolic 3-manifold by Dehn fillings. It is shown that for any such non-trivial element, there are only finitely many Dehn fill...
The 2nd Pan Pacific International Conference on Topology and Applications 2017年11月15日
I will talk about an algorithm to build 3-manifolds with closed separating in- compressible surfaces and about thin position method to study such surfaces and Heegaard splittings.
本研究では,3次元多様体内の結び目に関する矯飾的手術予想(Cosmetic Surgery Conjecture)「結び目に沿った異なるデーン手術によって(向きも込めて) 同相な3次元多様体は生成されないだろう」の肯定的解決にむけて研究を行う。具体的な目標は,3次元球面内の交代結び目に関して肯定的解決を得ることである。
