J-GLOBAL         Last updated: Sep 2, 2017 at 02:59
Alternative names
Nihon University
College of Humanities and Sciences, Department of Mathematics
Job title
Doctor of Science(Tokyo Institute of Technology)
Research funding number

Research Areas


Academic & Professional Experience

Apr 2002
Mar 2004
Research Fellow (Post Doc), Nara Women's University, the Japan Society for the Promotion of Science
Apr 2004
Mar 2007
Lecturer, College of General Education, Osaka Sangyo Univrsity
Apr 2007
Mar 2010
Associate Professor, Nara University of Education
Apr 2010
Mar 2013
Associate Professor, Department of Mathematics, College of Humanities and Sciences, Nihon University.
Apr 2013
Professor, Department of Mathematics, College of Humanities and Sciences, Nihon University.


Apr 1991
Mar 1995
Department of Mathematics, Faculty of Science and Engineering, Keio University
Apr 1995
Mar 1997
Department of Mathematics, Graduate School, Division of Science and Engineering, Tokyo Institute of Technology
Apr 1997
Mar 2000
Department of Mathematics, Graduate School, Division of Science and Engineering, Tokyo Institute of Technology

Awards & Honors

Sep 2002
Takebe Junior Prize awarded by the Mathematical Society of Japan

Published Papers

Kazuhiro Ichihara, Eri Matsudo
Journal of Knot Theory and Its Ramifications   26 1750018-1-1750018-23   Feb 2017   [Refereed]
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
Kazuhiro Ichihara, Eri Matsudo
Kobe Journal of Mathematics   33(1-2) 53-60   Dec 2016   [Refereed]
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.
Kazuhiro Ichihara, Hidetoshi Masai
Communications in Analysis and Geometry   24(2) 337-377   Jun 2016   [Refereed]
We give a complete classification of exceptional surgeries on hyperbolic alternating knots in the 3-sphere. As an appendix, we also show that the Montesinos knots M(−1/2,2/5,1/(2q+1)) with q > 4 have no non-trivial exceptional surgeries. This give...
Neil Hoffman, Kazuhiro Ichihara, Masahide Kashiwagi, Hideyoshi Masai,Shin’ichi Oishi, Akitoshi Takayasu
Experimental Mathematics   25(1) 66-78   Jan 2016   [Refereed]
For a given cusped 3-manifold admitting an ideal triangulation, we describe a method to rigorously prove that either the manifold or a filling of the manifold admits a complete hyperbolic structure via verified computer calculations. Central to o...
Kazuhiro Ichihara, Makoto Mori, and Ken-ichi Yoshida
RIMS Kôkyûroku   1960 1-17   Aug 2015
We consider the random link, which is defined as the closures of braids obtained from random walks on the braid groups. For random links, the expected value for the number of components were calculated by Jiming Ma. In this article, we report on t...


Bounds on boundary slopes for knots
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.

Conference Activities & Talks

Kazuhiro Ichihara
30 Aug 2017   
Kazuhiro Ichihara
Differential Topology 17   29 Mar 2017   
The well-known L-space conjecture saids that an irreducible rational homology 3-sphere is an L-space if and only if its fundamental group is not left-orderable. One of the known approaches to the conjecture is by using Dehn surgery. In this talk, ...
Kazuhiro Ichihara
Invariants of 3-manifolds related to the Casson invariant   26 Jan 2017   Research Institute for Mathematical Sciences, Kyoto University
I will talk about two generalizations of the Casson invariant, and their applications to the cosmetic surgery conjecture on knots. One is the SL(2,C) version of the Casson invariant originally introduced by Curtis, and the other is the degree 2 pa...
Kazuhiro Ichihara, Toshio Saito
Fundamental Groups, Representations and Geometric Structures in 3-Manifold Topology   22 Nov 2016   
I will talk about the SL(2, C) Casson invariant for 3-manifolds, and its applications to the cosmetic surgery problem for knots in the 3- sphere. In particular, in terms of boundary slopes, a condition for knots to admit no cosmetic surgeries will...
Kazuhiro Ichihara
Tohoku Knot Seminar   16 Oct 2016   
It was conjectured by L.M. Lopez that small knots always exist in closed small 3-manifolds. In this talk, I will talk about the current status of this conjecture, and show that every lens space contains a hyperbolic small knot.

Research Grants & Projects

Project Year: Apr 2014 - Mar 2017    Investigator(s): Kazuhiro Ichihara