Study of Roseman moves using quandle theory and immersion theory

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400082
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Tokyo Gakugei University
• Principal Investigator: Tanaka Kokoro 東京学芸大学, 教育学部, 准教授 (70448950)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 位相幾何 / 曲面結び目 / ローズマン変形 / カンドル / はめ込み

Outline of Final Research Achievements

We studied independence of Roseman moves for surface-knot diagrams. Firstly, using immersion theory, we shed light on independence of Roseman moves including branch points. More pricisely, we constructed a pair of two 2-knots such that any sequence of Roseman moves between them contains branch points. Secondly, using quandle theory, we shed light on independence of Roseman moves including triple points. More pricisely, we constructed a pair of two 2-knots such that any sequence of Roseman moves between them contains triple points.

Free Research Field

数物系科学