J-GLOBAL         Last updated: Dec 3, 2019 at 02:47
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, 教育学部 数学教育講座, Nara University of Education
Apr 2010
Mar 2013
Associate Professor, Department of Mathematics, College of Humanities and Sciences, Nihon University.
Sep 2011
Mar 2012
非常勤講師, 法学部, 慶應義塾大学
Apr 2013
Professor, Department of Mathematics, College of Humanities and Sciences, Nihon University.
Jul 2014
Aug 2014
平成26年度 短期B海外派遣研究員, 日本大学
Jul 2014
Aug 2014
Visitor (Academic), Department of Mathematics and Statistics, Faculty of Science, The University of Melbourne
Apr 2016
Apr 2016
Academic Visitor, Department of Mathematics, The Chinese University of HongKong
Jul 2018
Aug 2018
平成30年度 短期B海外派遣研究員, 日本大学


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
3次元多様体のデーン手術と本質的曲面の研究, Takebe Junior Prize awarded by the Mathematical Society of Japan

Published Papers

Kazuhiro Ichihara, Zhongtao Wu
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...
Kazuhiro Ichihara, Kimihiko Motegi, Masakazu Teragaito
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...
Kazuhiro Ichihara, In Dae Jong, Kouki Taniyama
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 ...


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.

Books etc

大石 進一 (著, 編集), 荻田 武史 (著), 柏木 雅英 (著), 劉 雪峰 (著), 尾崎 克久 (著), 山中 脩也 (著), 高安 亮紀 (著), 関根 晃太 (著), 木村 拓馬 (著), 市原 一裕 (著), 正井 秀俊 (著), 森倉 悠介 (著), Siegfried M. Rump (著) (Part:Joint Work, 9.3 3次元多様体の双曲性判定)
コロナ社   Jul 2018   ISBN:978-4339028874
市原 一裕,鈴木 正彦,茂手木 公彦 (Part:Joint Work)
日本評論社   Mar 2018   ISBN:978-4535788596
数学セミナー編集部 (編集)
日本評論社   Mar 2018   
技術評論社   Jan 2018   ISBN:978-4-7741-9478-3
数学セミナー編集部 (編集)
日本評論社   Mar 2017   
永井 均 (著), 古川 隆久 (著), 佐藤 至子 (著), 三澤 真美恵 (著), マイルズ・チルトン (著), 初見 基 (著), 久保田 裕之 (著), 金子 絵里乃 (著), 広田 照幸 (著), 青山 清英 (著), 菊島 勝也 (著), 矢ケ﨑 典隆 (著), 安井 真也 (著), 市原 一裕 (著), 尾崎 知伸 (著), 十代 健 (著), 間瀬 啓介 (著), 大﨑 愛弓 (著), 日本大学文理学部 (編集) (Part:Joint Work, 第14講 数学は宇宙の謎を解くか)
筑摩書房   Feb 2017   ISBN:978-4-480-06942-9
数学セミナー編集部 (編集)
日本評論社   Mar 2016   
下川航也 (Part:Joint Work)
数学書房   Dec 2010   ISBN:978-4-903342-46-7
丸本 嘉彦; 張替 俊夫; 田村 誠; 市原 一裕; (Part:Joint Work)
共立出版   Dec 2007   ISBN:978-4320018549
大学工学部初年度生を対象とした,線形代数学の教科書.予備知識をあまり仮定せず,練習問題を多く含むようにし,自 学自習用にも使えるように配慮した.

Conference Activities & Talks

Kazuhiro Ichihara
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...
Kazuhiro Ichihara
Extended KOOK Seminar 2019   21 Aug 2019   
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...
Kazuhiro Ichihara
MSJ Spring Meeting 2019   19 Mar 2019   Mathematical Society of Japan
In this talk, we report on our results on separating incompressible surfaces and incompressible subsurfaces of Heegaard surfaces in a 3-manifold.
Kazuhiro Ichihara
Geometric Topology of low dimensions   9 Mar 2019   
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.
Kazuhiro Ichihara
研究集会『結び目の数理』   25 Dec 2018   
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...

Research Grants & Projects

Project Year: Apr 2018 - Mar 2022    Investigator(s): Kazuhiro Ichihara
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。