| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
1. I defined the notion of a module over a manifold endowed with the structure of a quandle (quandle manifold), and provided various examples. Then, in the case the quandle manifold is a ``regular s-manifold'', I defined regular modules, and showed that they correspond to regular representations of a certain algebra, called an infinitesimal s-manifold. Furthermore, I arrived at an outlook on how they relate to representations of the relevant Lie algebra.
2. I obtained results on how to associate a quandle or a multiple conjugation quandle to an integer ring, and how the integer ring can be reconstructed.
3. I studied logarithmic BPS invariants and logarithmic Gromov-Witten invariants; how they are related to local BPS invariants; a conjecture that they are independent of the point of contact; the contribution of a degenerate curve.
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