2012 Fiscal Year Final Research Report
Study on quandle theory to classifying links up to link-homotopy
| Project/Area Number |
23840014
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
INOUE Ayumu 東京工業大学, 大学院・情報理工学研究科, 科学研究費教育研究支援員 (10610149)
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| Project Period (FY) |
2011 – 2012
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| Keywords | トポロジー / 絡み目 / カンドル / 絡み目ホモトピー |
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| Research Abstract |
Link-homotopy gives rise to an equivalence relation on links which is weaker than ambient isotopy. A quandle is an algebraic system which is known to be useful to classifying links up to ambient isotopy. The aim of this study is to utilize quandles to classifying links up to link-homotopy. We introduced the notion of quasi-triviality of quandles, homology theory for quasi-trivial quandles, and obtained a lot of numerical link-homotopy invariants. We further explained the latent ability of those invariants.
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