Geometry on concordance invariants of knots and links

2017 Fiscal Year Final Research Report

• Project/Area Number: 24540074
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Nagoya University
• Principal Investigator: Kawamura Tomomi 名古屋大学, 多元数理科学研究科, 准教授 (40348462)
• Project Period (FY): 2012-04-01 – 2018-03-31
• Keywords: 結び目と絡み目 / 結び目と絡み目の射影図 / ラスムッセン不変量 / オジュバットとサボーの結び目不変量 / プレッツェル結び目 / ザイフェルト曲面 / 種数あるいはオイラー数 / 橋の架け替え

Outline of Final Research Achievements

A knot or link is a closed curve or its copies in the 3-dimensional space. An invariant of a knot or link is the number or something representing how complex it is. Many invariants have been constructed.
In this research, we determine the Rasmussen invariant and the Ozsvath-Szabo invariant for certain pretzel knots. Furthermore we show a bridge-replacing move induced on knot diagrams is as useful in computing the Euler characteristic of a link, a kind of link invariants, as the genus of a knot, a kind of knot invariants.

Free Research Field

結び目理論と低次元トポロジー