| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
The results obtained in the project are followings.
It is known that total spaces of torus bundles over the torus with sections admit genus-3 Lefschetz pencils. In this project we first determine vanishing cycles of holomorphic pencils on the four-torus. We further construct Lefschetz pencils on manifolds homeomorphic to total spaces of torus bundles over the torus.
Recently, Gay and Kirby defined a trisection, which gives rise to a diagram describing a four-manifold. Trisections are related to stable mappings from four-manifolds to the plane. In analyzing stable mappings, Baykur and Saeki introduced a notion of simplified trisections and gave several examples of them. Relying on the theory of mapping class groups of surfaces, we give an algorithm to obtain diagrams associated with simplified trisections.
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