2012 Fiscal Year Final Research Report
Topological properties of knots and surfaces through splicing and deformations
| Project/Area Number |
22740038
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Nagoya Institute of Technology |
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Principal Investigator |
HIRASAWA Mikami 名古屋工業大学, 工学研究科, 准教授 (00337908)
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| Co-Investigator(Renkei-kenkyūsha) |
MURASUGI Kunio トロント大学, 数学科, 名誉教授
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| Project Period (FY) |
2010 – 2012
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| Keywords | 結び目理論 / アレキサンダー多項式 / ファイバー結び目 |
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| Research Abstract |
A tangled circle in the 3-space is called a knot, and we regard two knots to be equivalent when they can be deformed continuously into each other. One of the most important topological invariants of knots is the Alexander polynomial. We studied the distribution of zeros of the Alexander polynomials of knots, and by using Seifert surfaces, we obtained results on various stability properties. We also studied deformation of surfaces from the viewpoint of their contours. As a result, we gave a new visualization of the sphere eversion by regular isotopy.
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