Finite type invariants and Milnor invariants by clasper theory
Project/Area Number |
16K17586
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Geometry
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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
|
Project Status |
Completed (Fiscal Year 2020)
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Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
|
Keywords | 位相幾何学 / 結び目理論 / 絡み目 / ミルナー不変量 / ハンドル体絡み目 / Vassiliev不変量 / Goussarov-Polyak-Viro不変量 / 仮想結び目 / 絡み目ホモトピー / クラスパー理論 / 有限型不変量 / 仮想絡み目 / クラスパー / Milnor不変量 |
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.
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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.
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Report
(6 results)
Research Products
(47 results)