| Project/Area Number |
18K13419
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 11020:Geometry-related
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| Research Institution | Okinawa Institute of Science and Technology Graduate University |
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Principal Investigator |
KHANDHAWIT TIRAS 沖縄科学技術大学院大学, 多様体のトポロジーとジオメトリーユニット, 研究員 (40721840)
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| Project Period (FY) |
2018-04-01 – 2020-03-31
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| Project Status |
Discontinued (Fiscal Year 2018)
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| Budget Amount *help |
¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | Seiberg-Witten theory / Low-dimensional topology / Stable homotopy theory / 低次元トポロジー / ゲージ理論 / Seiberg-Witten Theory / Stable homotopy |
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| Outline of Annual Research Achievements |
One of the major research achievements is rigorous construction of relative Bauer-Furuta invariants and proof of the gluing theorem. The theorem generalizes to larger classes of manifolds. There are some direct application to compute Bauer-Furuta invariant of a 4-manifold after doing surgery as well as to find a condition for having embedded 2-sphere in term of Bauer-Furuta invariant.
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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
The proof of the gluing theorem is quite long very technical. As we have completed the proof early, we have more opportunities to study further directions.
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| Strategy for Future Research Activity |
After establishing the gluing theorem, there are many possible directions and applications to explore. In a work with Hokuto Konno, we try to consider a family version of Bauer-Furuta invariant. In a work with Donghao Wang, we try to apply the gluing theorem in a case when a boundary manifold is a 3-torus.
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