Communications in Analysis and Geometry 27(5) 1087-1104 Nov 2019 [Refereed]
We show that two Dehn surgeries on a knot K never yield manifolds that are homeomorphic as oriented manifolds if V′′K(1)≠0 or V′′′K(1)≠0. As an application, we verify the cosmetic surgery conjecture for all knots with no more than 11 crossings ex...
Topology and its Applications 264 223-232 Sep 2019 [Refereed]
We prove that for any hyperbolic knot and any nontrivial element in the knot group, there are only finitely many Dehn fillings of the knot exterior which trivialize the element. We also demonstrate that there are infinitely many nontrivial element...
Kazuhiro Ichihara, Makoto Ozawa, and J. Hyam Rubinstein
Topology and its Applications 264 21-26 Sep 2019 [Refereed]
In this paper, by putting a separating incompressible surface in a 3-manifold into Morse position relative to the height function associated to a strongly irreducible Heegaard splitting, we show that an incompressible subsurface of the Heegaard sp...
Lobachevskii Journal of Mathematics 39(9) 1353-1361 Jan 2019 [Refereed]
It is experimentally known that achiral hyperbolic 3-manifolds are quite sporadic at least among those with small volume, while we can find plenty of them as amphicheiral knot complements in the 3-sphere. In this paper, we show that there exist in...
Kazuhiro Ichihara, In Dae Jong and Hidetoshi Masai
Osaka Journal of Mathematics 55(4) 731-745 Oct 2018 [Refereed]
We present various examples of cosmetic bandings on knots and links, that is, bandings on knots and links leaving their types unchanged. As a byproduct, we give a hyperbolic knot which admits exotic chirally cosmetic surgeries yielding hyperbolic ...
Journal of Osaka Sangyo University. Natural sciences 117 33-43 Feb 2006
In this research note, a number of bounds on boundary slopes of essential surfaces embedded or immersed in 3-manifolds are presented. Also reports on computer- aided experiments, concerning embedded boundary slopes for Montesinos knots, are included.
International Workshop ''Knots in Tsushima 2019'' 7 Sep 2019
In this talk, I will talk about the minimal number of colors for non-trivial Z-colorings on the standard minimal diagrams of Z-colorable torus links. This talk is based on a joint work with Katsumi Ishikawa (RIMS, Kyoto Univ) and Eri Matsudo (Niho...
In this talk, I will report our recent result on a complete list of hyperbolic two-bridge links which can admit complete exceptional surgeries. This is based on a joint work with Jong In Dae (Kindai University) and Hidetoshi Masai (Tokyo Institute...
The aim of the talk is to introduce various (purely or chirally) cosmetic bandings on knots, that is, bandings on knots unchanging the knot types, and to explain, for a given cosmetic banding, the reason why the banding is cosmetic.
I will talk about random graphs and consider the intrinsically knotted/linked properties. It will be shown that the probability that a graph is intrinsically knotted goes to one as the number of vertices increases, and also that most graphs with s...
Project Year: Apr 2014 - Mar 2017 Investigator(s): Kazuhiro Ichihara
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。
