Development of tangle-method in surface-knot theory and its applications
| Project/Area Number |
25400090
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Kobe University |
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Principal Investigator |
Satoh Shin 神戸大学, 理学(系)研究科(研究院), 教授 (90345009)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 曲面タングル / 曲面結び目 / 溶接結び目 / フォックス彩色 / デーン彩色 / 節付き結び目 / 結び目解消操作 / タングル分解 / 仮想結び目 / ステイト数 |
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| Outline of Final Research Achievements |
A surface-knot is a closed surface embedded in 4-space. We study many properties of surface-knots from the viewpoint of surface-tangles and local moves. We characterize a surface-knot which has a decomposition of trivial surface-tangles, and prove the splittability of a surface-tangle with fabric structure.
On the other hand, we also study many properties of virtual knots and welded knots which present surface-knots of genus one. We characterize a virtual knot whose 3-state number is zero, and determine the minimal number of colors needed for effective Fox or Dehn colorings for a knot or surface-knot. We also prove that the crossing change and delta-move on a welded knot are both an unknotting operation.
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Report
(4 results)
Research Products
(29 results)
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[Presentation] 結び目のステイト数2014
Author(s)
佐藤進
Organizer
写像の特異点論及び関連する科学の諸問題
Place of Presentation
都城工業高等専門学校
Year and Date
2014-06-05
Related Report
Invited
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