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DAE JONG In

    Department of Science　Associate Professor
Last Updated :2024/04/23

Researcher Information

J-Global ID

Research Interests

  • alternating knot   Alexander polynomial   Dehn surgery   Geometry   knot   Topology   

Research Areas

  • Natural sciences / Geometry

Published Papers

  • Kazuhiro Ichihara; In Dae JONG
    preprint, arXiv:2401.07269 [math.GT] 2024/01
  • An integral region choice problem with two prohibited regions
    Yamato Fukushima; In Dae JONG
    preprint 2023
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  • Kazuhiro Ichihara; In Dae Jong; Thomas W. Mattman; Toshio Saito
    Algebraic and Geometric Topology Mathematical Sciences Publishers 21 (5) 2411 - 2424 1472-2747 2021 [Refereed]
     
    We show that two-bridge knots and alternating fibered knots admit no purely cosmetic surgeries, i.e., no pair of distinct Dehn surgeries on such a knot produce 3-manifolds that are homeomorphic as oriented manifolds. Our argument, based on a recent result by Hanselman, uses several invariants of knots or 3-manifolds; for knots, we study the signature and some finite type invariants, and for 3-manifolds, we deploy the SL(2,ℂ) Casson invariant.
  • Kazuhiro Ichihara; In Dae Jong; Hidetoshi Masai
    Kodai Mathematical Journal (to appear) 2019/09 [Refereed]
     
    We give a complete list of hyperbolic two-bridge links which can admit complete exceptional surgeries. Whole of candidates of surgery slopes of them are also given.
  • Kazuhiro Ichihara; In Dae Jong; Kouki Taniyama
    Lobachevskii Journal of Mathematics 39 (9) 1353 - 1361 2018/11 [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 infinitely many achiral 1-cusped hyperbolic 3-manifolds not homeomorphic to any amphicheiral null-homologous knot complement in any closed achiral 3-manifold.
  • Kazuhiro Ichihara; In Dae Jong; Hidetoshi Masai
    Osaka Journal of Mathematics 55 (4) 731 - 745 2018/10 [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 manifolds. This gives a counterexample to a conjecture raised by Bleiler, Hodgson and Weeks.
  • Tetsuya Abe; In Dae Jong; John Luecke; John Osoinach
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES OXFORD UNIV PRESS (22) 11667 - 11693 1073-7928 2015 [Refereed]
     
    We prove that for any integer n there exist infinitely many different knots in S-3 such that n-surgery on those knots yields the same 3-manifold. In particular, when vertical bar n vertical bar = 1 homology spheres arise from these surgeries. This answers Problem 3.6(D) on the Kirby problem list. We construct two families of examples, the first by a method of twisting along an annulus and the second by a generalization of this procedure. The latter family also solves a stronger version of Problem 3.6(D), that for any integer n, there exist infinitely many mutually distinct knots such that 2-handle addition along each with framing n yields the same 4-manifold.
  • Kazuhiro Ichihara; In Dae Jong
    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES JAPAN ACAD 90 (3) 54 - 56 0386-2194 2014/03 [Refereed]
     
    We give a complete classification of toroidal Seifert fibered surgeries on alternating knots. Precisely, we show that if an alternating knot K admits a toroidal Seifert fibered surgery, then K is either the trefoil knot and the surgery slope is zero, or the connected sum of a (2,p)-torus knot and a (2, q)-torus knot and the surgery slope is 2(p + q) with vertical bar p vertical bar, vertical bar q vertical bar >= 3.
  • On positive knots of genus two
    In Dae Jong; Kengo Kishimoto
    Kobe Journal of Mathematics 30 (1--2) 1 - 18 2013/11 [Refereed]
     
    We show that positive knots of genus two are positive-alternating or almost
    positive-alternating. We also show that positive knots of genus two are quasialternating.
    In addition, we show that every prime positive knot of genus two is obtained
    from one of certain fourteen positive diagrams by t′2 moves.
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  • Tetsuya Abe; In Dae Jong; Yuka Omae; Masanori Takeuchi
    Mathematical Proceedings of the Cambridge Philosophical Society 155 (2) 219 - 235 0305-0041 2013/09 [Refereed]
     
    We give a method for obtaining infinitely many framed knots which represent a diffeomorphic 4-manifold. We also study a relationship between the n-shake genus and the 4-ball genus of a knot. Furthermore we give a construction of homotopy 4-spheres from a slice knot with unknotting number one. © 2013 Cambridge Philosophical Society.
  • Kazuhiro Ichihara; In Dae Jong
    GEOMETRY AND TOPOLOGY DOWN UNDER AMER MATHEMATICAL SOC 597 (2013) 321 - 336 0271-4132 2013 [Refereed]
     
    We give a new criterion for a given knot to be a Montesinos knot by using the Rasmussen invariant and the signature. We apply the criterion to study Seifert fibered surgery on a strongly invertible knot, and show that a (p, q, q)-pretzel knot with integers p, q >= 2 admits no Seifert fibered surgery.
  • Kazuhiro Ichihara; In Dae Jong; Yuichi Kabaya
    TOPOLOGY AND ITS APPLICATIONS ELSEVIER SCIENCE BV 159 (4) 1064 - 1073 0166-8641 2012/03 [Refereed]
     
    We give a complete description of exceptional surgeries on pretzel knots of type (-2, p, p) with p >= 5. It is known that such a knot admits a unique toroidal surgery yielding a toroidal manifold with a unique incompressible torus. By cutting along the torus, we obtain two connected components, one of which is a twisted I-bundle over the Klein bottle. We show that the other is homeomorphic to the one obtained by certain Dehn filling on the magic manifold. On the other hand, we show that all such pretzel knots admit no Seifert fibered surgeries. (C) 2011 Elsevier B.V. All rights reserved.
  • In Dae Jong
    TOPOLOGY AND ITS APPLICATIONS ELSEVIER SCIENCE BV 159 (4) 1007 - 1015 0166-8641 2012/03 [Refereed]
     
    In the previous paper, the author gave linear inequalities on the coefficients of the Alexander polynomials of alternating knots of genus two, which are best possible as linear inequalities on the coefficients of them. In this paper, we give infinitely many Alexander polynomials which satisfy the linear inequalities, but they are not realized by alternating knots. (C) 2011 Elsevier B.V. All rights reserved.
  • Kazuhiro Ichihara; In Dae Jong
    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES JAPAN ACAD 87 (2) 17 - 21 0386-2194 2011/02 [Refereed]
     
    We introduce new simplicial complexes by using various invariants and local moves for knots, which give generalizations of the Gordian complex defined by Hirasawa and Uchida. In particular, we focus on the simplicial complex defined by using the Alexander-Conway polynomial and the Delta-move, and show that the simplicial complex is Gromov hyperbolic and quasi-isometric to the real line.
  • In Dae Jong
    Journal of Knot Theory and its Ramifications 19 (8) 1075 - 1092 1793-6527 2010/08 [Refereed]
     
    We give a family of linear inequalities which strictly estimate relation among the coefficients of the Alexander polynomials of alternating knots of genus two. We also give such families for positive knots of genus two, and for homogeneous knots of genus two. As an application, we determine the alternating knots of genus two such that the leading coefficients of them are less than or equal to three.
  • Kazuhiro Ichihara; In Dae Jong
    COMMUNICATIONS IN ANALYSIS AND GEOMETRY INT PRESS BOSTON, INC 18 (3) 579 - 600 1019-8385 2010/07 [Refereed]
     
    We show that if a Montesinos knot admits a Dehn surgery yielding a toroidal Seifert fibered 3-manifold, then the knot is the trefoil knot and the surgery slope is 0.
  • In Dae Jong
    OSAKA JOURNAL OF MATHEMATICS OSAKA JOURNAL OF MATHEMATICS 46 (2) 353 - 371 0030-6126 2009/06 [Refereed]
     
    We confirm R.H. Fox's trapezoidal conjecture for alternating knots of genus two by a method different from P. Ozsvath and Z. Szabo's one. As an application, we determine the alternating knots of genus two whose Alexander polynomials have minimal coefficients equal to one or two.
  • Kazuhiro Ichihara; In Dae Jong
    ALGEBRAIC AND GEOMETRIC TOPOLOGY GEOMETRY & TOPOLOGY PUBLICATIONS 9 (2) 731 - 742 1472-2739 2009 [Refereed]
     
    We give a complete classification of the Dehn surgeries on Montesinos knots which yield manifolds with cyclic or finite fundamental groups.

Books etc

Conference Activities & Talks

Research Grants & Projects

  • 日本学術振興会：科学研究費助成事業
    Date (from‐to) : 2022/04 -2027/03 
    Author : 鄭 仁大
  • 日本学術振興会：科学研究費助成事業
    Date (from‐to) : 2019/04 -2023/03 
    Author : 鄭 仁大
     
    ２橋結び目や２橋絡み目，交代結び目，モンテシノス結び目に沿ったデーン手術に関する研究を行い，以下に述べる研究成果を得ることができました． １）任意の非自明な２橋結び目は，純コスメティック手術対，つまり，２つの異なるスロープに沿ったデーン手術の対で，向きを込めて同相な3次元多様体を生むようなもの，を許容しないことを証明した論文（市原一裕氏（日本大学），斎藤敏夫氏（上越教育大学），Thomas Mattman 氏（California state University, Chico）との共著論文）が学術雑誌 Algebraic and Geometric Topology の21巻5号に掲載されました．その論文においては，全ての交代的ファイバー結び目および交代的プレッツェル結び目についても，コスメティック手術予想に対する肯定的な解答を得ています． ２）交代結び目，およびモンテシノス結び目が純コスメティック手術をもつための障害となる不変量の計算を行い，これらの結び目に対する純コスメティック手術予想の部分的な解答を得ました．具体的には，コンウェイ多項式の２次の係数．ならびに次数３の有限型不変量に関する計算を行い，交代結び目，またはモンテシノス結び目で純コスメティック手術を許容するクラス（無限族）を有限個まで制限することができました．交代結び目については２種類のクラスに制限できました．この研究については市原一裕氏(日本大学)との共同研究であり，現在も引き続き研究を進めています．
  • Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research
    Date (from‐to) : 2012/04 -2017/03 
    Author : KAWAUCHI Akio; KAMADA Seiichi; SAKUMA Makoto; NAKANISHI Yasutaka; TANIYAMA Kouki; OOYAMA Toshiyuki; MOTEGI Kimihiko; GOUDA Hiroshi; SHIMOKAWA Koya; TERAGAITO Masakazu; SATOU Shin; TANAKA Toshihumi; IWAKIRI Masahide; CHON Inde; KISHIMOTO Kengo; OTSUKI Tomotada; SHIMIZU Ayaka
     
    Using the knot as a key word, we have been working to encourage the development of mathematics in general, with a view of the related physics, chemistry and biology. Based on Osaka City University Mathematics Research Institute as an activity base and based on research cooperation agreements with 8 institutes in East Asia, we aimed to build a research network with Asia. We supported participation in many international or domestic regular meetings such as the satellite knot theory international conference of the Seoul International Congress of Mathematicians. Throughout these meetings, numerous important research results were obtained by a number of knot related researchers including research planning workers, which include research achievements obtaining two patents on the game "Region Select" applying the knot theory and solving a pending issue of 45 years of a ribbon 2-knot by the research representative.
  • Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research
    Date (from‐to) : 2010 -2011 
    Author : JONG In dae
     
    Ichihara and myself introduced new simplicial complexes by using various invariants and local moves for knots, which give generalizations of the Gordian complex. We focused on the simplicial complex defined by using the Alexander-Conway polynomial and the Delta-move, and showed that the simplicial complex is Gromov hyperbolic and quasi-isometric to the real line. I studied the characterization problem on the Alexander polynomial of an alternating knot. In particular, I constructed infinitely many Alexander polynomials which satisfy a necessary condition to become the Alexander polynomials of alternating knots but which cannot be realized by an alternating knot.

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