The existences of epimorphisms between knot groups and their geometric interpretations

2022 Fiscal Year Final Research Report

• Project/Area Number: 16K05159
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Meiji University
• Principal Investigator: Suzuki Masaaki 明治大学, 総合数理学部, 専任教授 (70431616)
• Project Period (FY): 2016-04-01 – 2023-03-31
• Keywords: 結び目群 / 全射準同型

Outline of Final Research Achievements

A knot is an embedded circle. The knot group of a knot is a fundamental group of the exterior of a knot. The fundamental group is the set of loops where two loops are considered as the same element if they are transformed continuously. The knot group characterizes a knot. However, it is very complicated. Then in this research, we considered whether there exists an epimorphism between knot groups and their geometric interpretations.

Free Research Field

位相幾何学

Academic Significance and Societal Importance of the Research Achievements

結び目群は結び目をとてもよく特徴づけているが、一般に群を調べることは容易ではないことが多い。そのため、その間の全射準同型の存在という関係を調べることは意味がある。このようにそのものが単独では複雑で扱いにくいものでも、それらの関係を調べるということで研究を進めるという方法は様々な場面で応用できるものと考えられ、その点でも意義があると考える。