Topology of stable mappings and diagrams of four-manifolds
| Project/Area Number |
26800027
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Keio University (2016-2017)
Hokkaido University (2014-2015) |
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Principal Investigator |
Hayano Kenta 慶應義塾大学, 理工学部(矢上), 講師 (20722606)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| 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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| Keywords | 安定写像 / 写像類群 / 消滅サイクル / trisection / モノドロミー / シンプレクティック多様体 / レフシェッツペンシル / ４次元トーラス / 偏極つきアーベル曲面 / ４次元多様体 |
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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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Report
(5 results)
Research Products
(23 results)
