A research of surface-links by using charts
| Project/Area Number |
23540107
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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 | Tokai University |
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Principal Investigator |
Shima Akiko 東海大学, 理学部, 教授 (50317765)
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| Project Period (FY) |
2011-04-28 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 曲面結び目 / チャート / 白頂点 / 交差 / トポロジー |
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| Outline of Final Research Achievements |
To classify surface-links, we make a table of surface-links by using charts. First we show that there is no minimal 4-chart nor minimal 5-chart which represent a sphere in 4-space. Next we show that any minimal chart with six white vertices contains one of six kinds of charts. Here a minimal chart means that the chart has the minimal number of crossings (or white vertices) among the charts C-move equivalent to the chart.
There are other moves between charts called a conjugation and a stabilization. To consider these moves, we define a CS-minimal chart. We show that any CS-minimal chart with exactly six white vertices is the product of a ribbon chart and a chart representing a 2-twist spun trefoil. To combine other results, we complete a classification of charts with at most seven white vertices module ribbon charts.
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Report
(6 results)
Research Products
(15 results)
