A characterization of a ribbon knot with property of surfaces in the knot complement

2018 Fiscal Year Final Research Report

• Project/Area Number: 16K05145
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Gifu University
• Principal Investigator: Tanaka Toshifumi 岐阜大学, 教育学部, 准教授 (60396851)
• Project Period (FY): 2016-04-01 – 2019-03-31
• Keywords: リボン結び目 / 曲面

Outline of Final Research Achievements

The purpose of this research is to characterize and classify ribbon knots in three-dimensional space by examining topological properties of curves appearing as the intersection of surfaces in the knot complement. It is expected that results can be obtained by examining the property of the curves that appears at the intersection of surfaces, which is a basic method of topology.
In this research, I studied a ribbon knot which is the main research object by studying surfaces in the knot complement. In particular, I studied a symmetric union, which is an example of a ribbon knot. As a result, I characterized surfaces in the knot complement in the case of composite knots or satellite knots for a symmetric union with minimum twist number one.

Free Research Field

トポロジー

Academic Significance and Societal Importance of the Research Achievements

補空間の曲面は，比較的扱いやすい多項式不変量に比べて，結び目のより詳細な情報をもつことが予想される。3次元空間における結び目の補空間の曲面を直接調べることによるスライス結び目の研究は，これまであまり行われていない。そのようなことから，本研究は成果はスライス結び目の幾何学的手法を用いた新たな研究手法に挑戦することにおいて，意義があると思われる。