Various invariants of 3 and 4-manifolds and their applicationsUe
| Project/Area Number |
16K05146
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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 | Kyoto University |
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Principal Investigator |
Ue Masaaki 京都大学, 理学研究科, 教授 (80134443)
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| Co-Investigator(Kenkyū-buntansha) |
加藤 毅 京都大学, 理学研究科, 教授 (20273427)
藤井 道彦 琉球大学, 理学部, 教授 (60254231)
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 4次元多様体 / 3次元多様体 / Seiberg-Witten理論 / Floerホモロジー / ザイフェルト多様体 / ３次元多様体 / ゲージ理論 / ザイフェルト３次元多様体 / Heegaard Floerホモロジー / 低次元トポロジー / ４次元多様体 |
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| Outline of Final Research Achievements |
We investigated the relation between invariants of 3-manifolds (in particular Seifert rational homology 3-spheres) which are defined combinatorially and those coming from gauge theories. These invariants are homology cobordism invariants, but other properties of them are mutually different. We heed further research about the relations between newly developed invariants and known results.
We almost completed writing the textbook about 4-dimensional topology written in Japanese, which includes
newly developed results about 4-manifolds as well as our own research results.
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| Academic Significance and Societal Importance of the Research Achievements |
3次元多様体のホモロジーコボルディズム不変量は近年活発に研究されており，その研究をさらに発展させることは，4次元トポロジー，特に境界付き4次元多様体の性質の解明にとって有用である．
また4次元トポロジーの教科書は基礎理論から類書にない近年の研究結果までを含んでおり，この分野の研究を総合的に知る上で有用なものになることが期待される．
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Report
(5 results)
Research Products
(5 results)
