Reconstruction of 2 and 3-dimensional closed manifolds by equi-dimensional stable maps and classification of embedding or immersion lifts
| Project/Area Number |
25800032
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Hirosaki University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 安定折り目写像 / はめ込み / レンズ空間 / ヒーガード分解 / 3次元閉多様体 / はめ込みリフト / コボルダント / 安定な折り目写像 / 向き付け可能な3次元閉多様体 / モース型の不等式 / はめ込みの拡張 / 折り目写像 |
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| Outline of Final Research Achievements |
The research leader studied constructions of stable fold maps of closed oriented 3-dimensional manifolds to the 3-space and lifts of these stable fold maps to immersions to the 4-space. The research results are as follows. (1): The leader constructed stable fold map of the lens space L(p, 1) to the 3-space whose singularity set is a torus. (2): The leader showed that an immersion lift of the stable fold map of the 3-sphere which was constructed in (1) to the 4-space is a generator of the cobordism group of the closed oriented 3-dimensional manifold to the 4-space.
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Report
(5 results)
Research Products
(9 results)
