2009 Fiscal Year Final Research Report
Study of local moves and invariants for knots and virtual knots
| Project/Area Number |
19540102
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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 | Tokyo Woman's Christian University |
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Principal Investigator |
OHYAMA Yoshiyuki Tokyo Woman's Christian University, 現代教養学部, 教授 (80223981)
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| Co-Investigator(Kenkyū-buntansha) |
KOBAYASHI Kazuaki 東京女子大学, 文理学部, 教授 (50031323)
OAKU Toshinori 東京女子大学, 現代教養学部, 教授 (60152039)
YOSHIARA Satoshi 東京女子大学, 現代教養学部, 教授 (10230674)
KODATE Takako 東京女子大学, 現代教養学部, 講師 (90317826)
NAKANISHI Yasutaka 神戸大学, 理学研究科, 教授 (70183514)
TANIYAMA kouki 早稲田大学, 教育・総合科学学術院, 教授 (10247207)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 結び目 / 空間グラフ / Vassiliev不変量 / C_n-move / C_n-distance |
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| Research Abstract |
We tie a knot and identify the end points of it. That figure having no end points is called "a knot" in Topology. A graph in R^3 is called a spatial graph. Two knots or spatial graphs are thought to be same if we transform one into another continuously in R^3 and the same mathematical value is made to correspond to the same knots or spatial graphs. The value is called an invariant. The finite type invariant is an invariant that classifies all the knot invariants by order. In this study, we define a new invariant for spatial graphs and investigate the property of it. For knots, we introduce the notion of a metric or a complex and we investigate the property of finite type invariants in the knot space.
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