2010 Fiscal Year Final Research Report
A study on invariants for knots derived from the magnetic graph
| Project/Area Number |
20540079
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Yamaguchi University |
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Principal Investigator |
MIYAZAWA Yasuyuki Yamaguchi University, 大学院・理工学研究科, 教授 (60263761)
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| Co-Investigator(Kenkyū-buntansha) |
SATO Yoshihisa 九州工業大学, 大学院・情報工学院, 教授 (90231349)
ANDO Yoshifumi 山口大学, 大学院・理工学研究科, 教授 (80001840)
NISHIYAMA Takahiro 山口大学, 大学院・理工学研究科, 准教授 (60333241)
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| Co-Investigator(Renkei-kenkyūsha) |
KOMIYA Katsuhiro 山口大学, 大学院・理工学研究科, 教授 (00034744)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 位相幾何 / 結び目理論 |
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| Research Abstract |
By using a graph diagram called a magnetic graph diagram which is a generalization of a knot diagram, we constructed a few new polynomial invariants for classical and virtual knots and showed that these polynomial invariants are very useful in classifying classical and virtual knots. Moreover, we found relationships between those invariants and a few geometric invariants by investigating properties of their invariants. They are important results which lead to analyze the structure of classical and virtual knots.
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