Finite type invariants and Milnor invariants by clasper theory

2020 Fiscal Year Final Research Report

• Project/Area Number: 16K17586
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Hiroshima University (2020); Institute of Physical and Chemical Research (2017-2019); The University of Tokyo (2016)
• Principal Investigator: Kotorii Yuka 広島大学, 先進理工系科学研究科(理), 准教授 (30737143)
• Project Period (FY): 2016-04-01 – 2021-03-31
• Keywords: 位相幾何学 / 結び目理論

Outline of Final Research Achievements

A link-homotopy is an equivalence relation on links generated by ambient isotopies and self-crossing changes. I constructed link-homotopy invariants for 4-component links and researched properties of link-homotopy classes of links by the invariants. I also researched properties of link-homotopy classes of handle-body links by making invariants. I also researched geometric properties of Goussarov-Polyak-Viro's finite type invariants on virtual links.

Free Research Field

低次元トポロジー

Academic Significance and Societal Importance of the Research Achievements

絡み目の不変量をクラスパー理論を用いてクラスパーの言葉で記述することで，図式的な計算が可能となり，計算の簡略化や新しい視点を導入することができる．本研究では，絡み目の絡み目ホモトピー不変量をクラスパーを用いて再定式化を与え，そこからさらに新しい不変量を構成した．このように，クラスパーを用いた定式化は，幾何的な視点からの新しい発展が期待される．