Study on local moves of knots with application to polymer topology

2016 Fiscal Year Final Research Report

• Project/Area Number: 24540089
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Osaka City University
• Principal Investigator: KANENOBU Taizo 大阪市立大学, 大学院理学研究科, 教授 (00152819)
• Project Period (FY): 2012-04-01 – 2017-03-31
• Keywords: 結び目 / 絡み目 / バンド手術 / 交差交換 / 多項式不変量 / DNA結び目

Outline of Final Research Achievements

We studied several local moves on knots and links such as a band surgery, crossing change, and SH(3)-move. We introduce further criteria to estimate the lower bound of the Gordian distances between two knots or links, which use the special values of the Jones, Q, and HOMFLYPT polynomials. Also, we gave criteria for the determinants between two links which are related by a band surgery, which come from the known criteria between two knots which are related by a crossing change. Then we gave a table of SH(3)-Gordian distances between knots with up to 7 crossings, we improved a table of H(2)-Gordian distances between knots with up to 7 crossings, we gave a table of Gordian distances between 2-component links with up to 6 crossings, and we improved a table of unknotting numbers of knots with up to 12 crossings.

Free Research Field

数学