鄭 仁大

J-GLOBALへ         更新日: 17/07/19 10:11
 
アバター
研究者氏名
鄭 仁大
 
チョン インデ
所属
近畿大学
部署
理工学部 理学科
職名
講師
学位
博士(理学)(大阪市立大学)
その他の所属
理工学部

研究分野

 
 

論文

 
市原 一裕, 鄭 仁大
to appear in Osaka Journal of Mathematics      [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 ...
Tetsuya Abe, In Dae Jong, John Luecke, John Osoinach
International Mathematics Research Notices      2015年2月   [査読有り]
We prove that for any integer n there exist infinitely many different knots in S3 such that n-surgery on those knots yields the same 3-manifold. In particular, when |n|=1 homology spheres arise from these surgeries. This answers Problem 3.6(D) on ...
市原 一裕, 鄭 仁大
Proceedings of the japan Academy, Series A, Mathematical Sciences   90(3) 54-56   2014年3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 KK admits a toroidal Seifert fibered surgery, then KK is either the trefoil knot and the surgery slope is ...
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...
安部 哲哉, 鄭 仁大, 大前 裕佳, 竹内 勝則
Mathematical Proceedings of the Cambridge Philosophical Society   155(3) 219-235   2013年9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...
市原 一裕, 鄭 仁大
Contemporary Mathematics   597(2013) 321-336   2013年8月   [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...
市原 一裕, 鄭 仁大, 蒲谷 裕一
Topology and its Applications   159(4) 1064-1073   2012年3月   [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...
鄭 仁大
Topology and its Applications   159(4) 1007-1015   2012年3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 infin...
市原 一裕, 鄭 仁大
Proceedings of the japan Academy, Series A, Mathematical Sciences   87(2) 17-21   2011年2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 A...
鄭 仁大
Journal of Knot Theory and its Ramifications   19(8) 1075-1092   2010年8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 o...
市原 一裕, 鄭 仁大
Communications in Analysis and Geometry   18(3) 579-600   2010年7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.
鄭 仁大
Osaka Journal of Mathematics   46(2) 353-371   2009年6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. Ozsváth and Z. Szabó's one. As an application, we determine the alternating knots of genus two whose Alexander polynomials have minimal c...
市原 一裕, 鄭 仁大
Algebraic and Geometric Topology   9(2) 731-742   2009年4月   [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.

講演・口頭発表等

 
市原 一裕, 鄭 仁大
拡大KOOKセミナー2016   2016年8月   
市原 一裕, 鄭 仁大
The 8th KOOK-TAPU Joint Seminar on Knots and Related Topics   2016年7月   
市原 一裕, 斎藤 敏夫, 鄭 仁大
日本数学会 2016年度年会   2016年3月16日   
The cosmetic surgery conjecture saids that no pair of Dehn surgeries along inequivalent slopes yield
orientation preservingly homeomorphic 3-manifolds. First I will tlak about a recent result on this conjecture
for certain two-bridge knots. Next I...
市原 一裕, 鄭 仁大
The 11th East Asian School of Knots and Related Topics   2016年1月28日   
A pair of Dehn fillings on a 3-manifold with a torus boundary
are called chirally cosmetic if the obtained pair of manifolds are orientation
reversingly homeomorphic. Cosmetic fillings on a 3-manifold are said to be
exotic if there is no self-home...
市原 一裕, 斎藤 敏夫, 鄭 仁大
東北結び目セミナー2015   2015年10月24日   
I will begin to give a brief survey on cosmetic surgery problem on knots. In particular,
the current status on Cosmetic Surgery Conjecture will be reported. After that, I will
present a potentially new construction of knots admitting an exotic cos...