Research on polymer topology via knot theory

2016 Fiscal Year Final Research Report

• Project/Area Number: 26800081
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Yamaguchi University
• Principal Investigator: Ishihara Kai 山口大学, 教育学部, 講師 (40634762)
• Research Collaborator: SHIMOKAWA Koya ; BUCK Dorothy ; RATHBUN Matthew ; VAZQUEZ Mariel ; ARUSUAGA Javier ; SOTEROS Chris
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: DNA結び目 / バンド手術 / 交差交換 / 格子結び目

Outline of Final Research Achievements

For application to studies of topology of polymers such as DNA and enzyme, we studied band surgeries and crossing changes on links, and studied lattice knots. In this project, we obtained the following results. First, we gave concrete pathways by band surgeries for each knot up to 7 crossings and each 2-component link up to 6 crossings. Also we showed that the pathways have diversity in general. Next, we gave a characterization for a single band surgery or a single crossing change between two fibered links. Some examples of band surgeries are determined by applying this result. Finally, we characterized lattice knots in a confined region.

Free Research Field

低次元トポロジー