topological properties of knots and surfaces

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400086
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Nagoya Institute of Technology
• Principal Investigator: Hirasawa Mikami 名古屋工業大学, 工学(系)研究科(研究院), 教授 (00337908)
• Co-Investigator(Renkei-kenkyūsha): YAMAMOTO Minoru 弘前大学, 教育学部, 准教授 (40435475)
• Research Collaborator: MURASUGI Kunio トロント大学, 名誉教授
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 結び目理論 / アレクサンダー多項式 / ザイフェルト曲面

Outline of Final Research Achievements

A tangled circle in the 3-space is called a knot, and a set of knots is called a link. we regard two knots to be equivalent when they can be deformed continuously into each other. We study topological properties of knots and links by orientable surfaces whose boundary coincide with them. We characterized tdistributions of the zeros of Alexander polynomial of Coxeter links corresponding to cycle graphs, and some specific arborescent links. For a given Alexander polynomial, we gave a simple and direct method to realize it by a knot.

Free Research Field

数物系科学