Interface between singularity theory of mappings and knot theory

2019 Fiscal Year Final Research Report

• Project/Area Number: 15K04880
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Seikei University
• Principal Investigator: Takase Masamichi 成蹊大学, 理工学部, 教授 (30447718)
• Co-Investigator(Kenkyū-buntansha): 渡邉 忠之 島根大学, 学術研究院理工学系, 講師 (70467447)
• Project Period (FY): 2015-04-01 – 2020-03-31
• Keywords: 中次元トポロジー

Outline of Final Research Achievements

I have been pursuing a new field of study lying between high dimensional topology and low dimensional topology and between differential topology and algebraic topology.
First, I studied the independence among the seven types of roseman moves in surface knot theory and published a joint paper with Dr. Kokoro Tanaka (Tokyo Gakugei University). Second, I studied the behaviour of complex tangents of smooth manifolds embedded in complex space and published two joint papers with Dr. Naohiko Kasuya (Kyoto Sangyo University). In addition, several projects, including a joint project with Dr. Tadayuki Watanabe (Shimane University), are underway.

Free Research Field

位相幾何学

Academic Significance and Societal Importance of the Research Achievements

これまでも「高次元トポロジー vs 低次元トポロジー」、「代数的トポロジー vs 微分トポロジー」、「PL トポロジー vs 微分トポロジー」という具合に分野横断的な研究を行ってきたが、本研究課題における成果はトポロジーをはみ出して複素微分幾何的な領域にまで広がってきた。このことは多様体のトポロジー、幾何学、ひいては数学の他分野への応用の幅を広げることに資する。