2016 Fiscal Year Final Research Report
Research on 3-manifold using geometric techniques and its development
| Project/Area Number |
25400091
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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 | Nara Women's University |
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Principal Investigator |
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| Research Collaborator |
BAKER Kenneth
FUNAKOSHI Yukari
HASHIZUME Megumi
IDO Ayako
ICHIHARA Kazuhiro
ITO Noboru
JANG Yeonhee
MURAI Hiroko
OZAWA Makoto
TAKAO Kazuto
RIECK Yo'av
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | 三次元多様体 / 結び目・絡み目 / Heegaard分解 / 橋分解 / 折り紙 / Hempel距離 / ミウラ折り |
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| Outline of Final Research Achievements |
In this research, we show that, for each n >1, there exist a Heegaard splitting with distance n, and there exists a bridge splitting with distance n. We introduce a new concept on Heegaard theory, called keen Heegaard splitting, and develop the techniques to show that there are keen Heegaard splittings with distance n. Then we show that there are knots each of which admits infinitely many irreducible bridge spheres with arbitrarily high bridge index. We apply the idea of similarity structure on 2-dimensional torus to construct flat foldable origami. Further we show that there are flat foldable origamis that are not constructed by using similarity structure. In addition to these, we define a distance on the set of isotopy classes of the spherical curves, and give some results on it.
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| Free Research Field |
幾何学
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