詳細

鄭　仁大 （チョン　インデ）

  • 理工学部 理学科　准教授
Last Updated :2024/04/25

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    空間内の絡まった紐（結び目）を対象に研究しています。特に結び目の様々な不変量や、結び目を用いた低次元トポロジーの研究を行っています。

研究者情報

学位

  • 博士（理学）（大阪市立大学）

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J-Global ID

研究キーワード

  • 交代結び目   アレクサンダー多項式   デーン手術   幾何学   結び目   トポロジー   

現在の研究分野（キーワード）

    空間内の絡まった紐（結び目）を対象に研究しています。特に結び目の様々な不変量や、結び目を用いた低次元トポロジーの研究を行っています。

研究分野

  • 自然科学一般 / 幾何学

研究活動情報

論文

  • 市原 一裕; 鄭 仁大
    preprint, arXiv:2401.07269 [math.GT] 2024年01月
  • An integral region choice problem with two prohibited regions
    福嶋 倭; 鄭 仁大
    preprint 2023年
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  • Kazuhiro Ichihara; In Dae Jong; Thomas W. Mattman; Toshio Saito
    Algebraic and Geometric Topology 21 5 2411 - 2424 2021年 [査読有り]
     
    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.
  • 市原一裕; 鄭仁大; 正井秀俊
    Kodai Mathematical Journal (to appear) 2019年09月 [査読有り]
     
    We give a list of hyperbolic two-bridge links which includes all such links with complete exceptional surgeries, i.e., Dehn surgeries on both components which yield non-hyperbolic manifolds but whose all the proper sub-fillings give hyperbolic manifolds. Also all the candidate slopes of complete exceptional surgeries for them are enumerated in our lists.
  • 市原 一裕; 鄭 仁大; 谷山 公規
    Lobachevskii Journal of Mathematics 39 9 1353 - 1361 2018年11月 [査読有り]
     
    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.
  • 市原 一裕; 鄭 仁大; 正井秀俊
    Osaka Journal of Mathematics 55 4 731 - 745 2018年10月 [査読有り]
     
    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 22 11667 - 11693 2015年 [査読有り]
     
    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 90 3 54 - 56 2014年03月 [査読有り]
     
    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
    鄭 仁大; 岸本 健吾
    Kobe Journal of Mathematics 30 1--2 1 - 18 2013年11月 [査読有り]
     
    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 2013年09月 [査読有り]
     
    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 597 2013 321 - 336 2013年 [査読有り]
     
    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 159 4 1064 - 1073 2012年03月 [査読有り]
     
    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 159 4 1007 - 1015 2012年03月 [査読有り]
     
    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 87 2 17 - 21 2011年02月 [査読有り]
     
    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.
  • 鄭 仁大
    Journal of Knot Theory and its Ramifications 19 8 1075 - 1092 2010年08月 [査読有り]
     
    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 18 3 579 - 600 2010年07月 [査読有り]
     
    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 46 2 353 - 371 2009年06月 [査読有り]
     
    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 9 2 731 - 742 2009年 [査読有り]
     
    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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