| Budget Amount *help |
¥16,120,000 (Direct Cost: ¥12,400,000、Indirect Cost: ¥3,720,000)
Fiscal Year 2014: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2013: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2012: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2011: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
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| Outline of Final Research Achievements |
We had established the fundamental theory of Lagrangian intersection Floer theory based on the filtered A infinity algebra in the last decade. In this research period, we studied its applications, especially to the mirror symmetry conjecture. We proved an ring isomorphism between the big quantum cohomology of any compact smooth toric manifold and the Jacobian ring of the potential function which we introduced from the context in the Lagrangian Floer theory. Moreover, we studied the correspondence of the Frobenius manifold structures between them. We went further to study of equivalence at (derived) categorical level, so called homological mirror symmetry conjecture. We showed generation criteria for the Fukaya category of compact symplectic manifold and obtained a generator for compact toric manifold. We used the virtual fundamental chain technique to obtain these results. For this purpose we also provided the technical details of the theory of Kuranishi structure and brushed it up.
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