Geometry on concordance invariants of knots and links

Research Project

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
Project Status	Completed (Fiscal Year 2017)
Budget Amount *help	¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000) Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000) Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000) Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000) Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000) Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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 / 種数 / ４次種数 / 絡み目コンコルダンス不変量 / 絡み目のホモロジー / オイラー数 / スライスオイラー数 / コバノフホモロジー / フレアーホモロジー / オジュバットとサボーの不変量 / ザイフェルト円周 / 結び目コンコルダンス不変量 / 絡み目のコボルディズム / 絡み目のスライスオイラー数 / ベネカン不等式 / ベネカン型不等式
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.