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DAE JONG In

    Department of Science　Associate Professor
Last Updated :2024/04/25

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.

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