Geometry in the interface between high- and low-dimensional Topology
| Project/Area Number |
19740031
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Shinshu University |
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Principal Investigator |
TAKASE Masamichi Shinshu University, 理学部, 准教授 (30447718)
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| Project Period (FY) |
2007 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥3,340,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | 低次元トポロジー / 微分可能写像 / 特異点 / 高次元結び目 / 埋め込み / はめ込み / コボルディズム / コボルデイズム / ホップ不変量 |
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| Research Abstract |
We show that any 3-sphere embedded in the 6-sphere can be obtained by performing the operation called spinning about submanifold, introduced by Dennis Roseman in 1989. Also, we analyze the possible values of a certain Hopf invariant, which is defined for such a 3-sphere embedded in the 6-sphere. And also, for a given immersion of the 3-sphere into the 4-space, we give a formula with which we can read off its bordism class from some geometric information on singularities of its extension by a generic map.
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Report
(5 results)
Research Products
(19 results)
