Award type：Award from Japanese society, conference, symposium, etc.  Country：Japan

Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

Web of Science

Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

Improving the slice-Bennequin inequality shown by Rudolph, we estimate some knot or link invariants, especially the knot invariant defined by Ozsváth and Szabó and the Rasmussen invariant for links introduced by Beliakova and Wehrli. Our argument implies a combinatorial proof of the slice-Bennequin inequality for links. Furthermore we determine such invariants for negative links and certain pretzel knots.

DOI： 10.1016/j.topol.2015.05.034

Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

Rasmussen introduced a knot invariant based on Khovanov homology theory, and showed that this invariant estimates the four-genus. We compare his result with the sharper slice-Bennequin inequality for knots. Then we obtain a similar estimate of the Rasmussen invariant to this inequality.

Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

As an extension of the class of algebraic links, A'Campo, Gibson, and Ishikawa constructed links associated to immersed compact one-manifolds in a two-dimensional disk, and particularly determined the gordian numbers for links of immersed arcs. We determine the gordian numbers for links associated with certain immersed circles.

Total pages：241   Responsible for pages：66--80   Language：Japanese

Authorship：Corresponding author   Language：English   Publishing type：Internal/External technical report, pre-print, etc.  

To appear in Osaka Journal of Mathematics

Event date： 2019.3

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Shimizu introduced a region crossing change unknotting operation for knot diagrams. As extensions, two integral region choice problems are proposed and the existences of solutions of the problems are shown for all non-trivial knot diagrams by Ahara and Suzuki, and Harada. We relate both integral region choice problems with an Alexander index for regions of a link diagram, and discuss the problems on link diagrams.

Event date： 2018.12

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Shimizu introduced a region crossing change unknotting operation for knot diagrams. As extensions, two integral region choice problems are proposed and the existences of solutions of the problems are shown for all non-trivial knot diagrams by Ahara and Suzuki, and Harada.
We relate both integral region choice problems with an Alexander index for regions of a link diagram, and discuss the problems on link diagrams.

Event date： 2013.9

Language：English   Presentation type：Oral presentation (invited, special)  

Country：Japan  

We estimate the knot invariant defined by Ozsv\'{a}th and Szab\'{o} and the Rasmussen invariant for links introduced by Beliakova and Wehrli. We determinate such invariants for negative links and certain Pretzel knots.

Event date： 2012.1

Language：Japanese   Presentation type：Oral presentation (invited, special)  

Venue：鹿児島大学理学部   Country：Japan  

接触構造の研究成果として有名なベネカン不等式と類似した評価式が多くの絡み目不変量に対して成立し精密化もなされている．本講演ではとくにスライスオイラー数、ラスムッセン不変量、オズバスとザボーの結び目不変量についての講演者の結果を紹介し、例として負の絡み目について不変量を決定する．

Event date： 2010.5

Language：English   Presentation type：Oral presentation (general)  

Country：Japan