Study on knots by diagrammatic approach

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K03492
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 11020:Geometry-related
• Research Institution: Kobe University
• Principal Investigator: Nakanishi Yasutaka 神戸大学, 理学研究科, 名誉教授 (70183514)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Keywords: 結び目 / 図式的アプローチ / 局所変形

Outline of Final Research Achievements

We have studied structures and invariants of knots by local moves to research the structure of knot space. We give a local move corresponding to writhe polynomial, which is a fundamental invariant of virtual knots. By considering this result, we give intersection polynomials, which are new invariants of virtual knots. Furthermore, we have studied their characters.

Free Research Field

位相幾何学

Academic Significance and Societal Importance of the Research Achievements

研究成果により結び目理論における新たな知見を与えることができた。この成果は結び目理論を通じて、位相幾何学ならびに数学の発展に寄与するものだと判断する。また、結び目の局所変形を通じて、DNA 結び目や高分子結び目の研究にも応用されることを期待している。