2022 Fiscal Year Final Research Report
Study of 3-dimensional topology with a pair of stable map to the plane and its fold map lift
| Project/Area Number |
20K03574
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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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| Review Section |
Basic Section 11020:Geometry-related
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| Research Institution | Hirosaki University |
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Principal Investigator |
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| Project Period (FY) |
2020-04-01 – 2023-03-31
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| Keywords | 折り目写像 / 安定写像 / リフト / ジェネリックホモトピー |
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| Outline of Final Research Achievements |
（1）I constructed a family of fold maps of lens space L(p,p-3) to the 3-space with two 2-spheres as singularity sets.
（2）I tried to construct a generic homotopy from a fold map with two 2-spheres as the singularity set to a fold map with one 2-sphere as the singular set. I was only able to construct it up to the halfway point and am still working on it.
（3）In the study of lifting a stable map from a closed 3-manifold to the plane to a fold map to the 3-space, I considered local liftability conditions. It turned out that it is necessary to describe global conditions for connecting local conditions together. I am continuing the work.
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| Free Research Field |
微分位相幾何学
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| Academic Significance and Societal Importance of the Research Achievements |
Morse関数や平面への安定写像を用いて，3次元多様体のトポロジーを研究する事は盛んに行われている．3次元空間への安定写像を用いる方法も少しずつ行われている．終域を3次元空間とした場合，・具体例が少ない・写像の全体像を記述するのが困難・写像の変形の様子も記述するのが困難，といった課題がある．研究継続中の成果が多くなってしまったが，今回の成果で3次元空間への安定折り目写像や安定写像を可視化する，1つの方法を提案することができた．
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