Bones about 4-dimensional differential structures and about Seifert surgeries
| Project/Area Number |
24840006
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | University of Tsukuba |
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Principal Investigator |
TANGE Motoo 筑波大学, 数理物質系, 助教 (70452422)
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| Project Period (FY) |
2012-08-31 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 4次元多様体 / 3次元多様体 / 結び目 / スライスリボン予想 / スライス結び目 / リボン結び目 / デーン手術 / ハンドル分解 / 最小種数 / トポロジー |
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| Research Abstract |
I studied some types of the local deformation of 4-manifolds by using Cork and Plug. I constructed infinitely many exotic structures with boundary by using my plug with infinitely order. Also, I considered other various deformation arising exotic structures. I found some negative-definite spin 4-manifolds for homology spheres. T.Abe and I studied slice-ribbon conjecture, as a result we found singularity sets generalizing ribbon singurality sets. We show the annulus twists for some 8_{20} gives ribbon knots.
Y.Yamada and I did research of lens space surgery. We analyzed the closed 4-manifolds obtained from torus knot and Berge's VII and VIII knot surgeries. I advanced the research of my classification problem of lens space surgery. I established the way to use continued fraction to prove the completeness of lens space suregery. K. Sato and I studied non-orientable genus in negative-definite 4-manifolds.
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Report
(3 results)
Research Products
(25 results)
