Relations between invariants of low-dimensional manifolds and their geometric structures
| Project/Area Number |
24540076
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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(系)研究科(研究院), 教授 (80134443)
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| Co-Investigator(Kenkyū-buntansha) |
Tsuyoshi Kato 京都大学, 理学研究科, 教授 (20273427)
Michihiko Fujii 京都大学, 理学研究科, 准教授 (60254231)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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 | 低次元トポロジー / 3次元多様体 / 4次元多様体 / Seiberg-Witten理論 / Heegaard Floerホモロジー / ザイフェルト多様体 / ホモロジーコボルディズム / ４次元多様体 / ３次元多様体 / エータ不変量 |
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| Outline of Final Research Achievements |
Ue studied invariants of 3-manifolds originated from the Seiberg-Witten and the Heegaard Floer homology theory. In particular in case of Seifert rational homology 3-spheres,which consist of special classes among 3-manifolds, he proved the mu-bar invariant (which is combinatorially defined) is represented by some combinations of analytically defined eta invariants under certain conditions using the Seiberg-Witten theory. He announced the above results at the conferences in Japan and overseas from 2012 to 2015 and completed the preprint (which is prepared to submit). He also continued to write a textbook on 4-manifolds, which started several years ago, including the latest achievements. He is trying to make the textbook in complete form within a year.
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Report
(5 results)
Research Products
(5 results)
