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2023 Fiscal Year Final Research Report

Lefschetz-Bott fibrations and convex symplectic manifolds

Research Project

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Project/Area Number 20K22306
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeMulti-year Fund
Review Section 0201:Algebra, geometry, analysis, applied mathematics,and related fields
Research InstitutionOsaka University (2021-2023)
Kyoto University (2020)

Principal Investigator

Oba Takahiro  大阪大学, 大学院理学研究科, 准教授 (50814464)

Project Period (FY) 2020-09-11 – 2024-03-31
KeywordsLefschetz-Bottファイバー空間 / シンプレクティック多様体 / 接触多様体 / 複素多様体
Outline of Final Research Achievements

We studied spaces called convex symplectic manifolds using Lefschetz-Bott fibrations. The main results are as follows: by using Lefschetz-Bott fibrations, we obtained a relation between two products of Dehn twists in the symplectic mapping class group of a 4-dimensional symplectic manifold. In addition, as a result of research derived from the study of Lefschetz-Bott fibrations, we characterized spheres of dimension 5 and higher with a geometric structure called the standard contact structure, based on their properties of dynamics and symplectic fillings.

Free Research Field

位相幾何学

Academic Significance and Societal Importance of the Research Achievements

Dehnツイストの積の間の関係式は曲面の写像類群の場合はよく研究されており,4次元シンプレクティック多様体の構成的な研究に用いられてきた.4次元以上のシンプレクティック多様体の写像類群においては,このような関係式はほとんど知られていない.本研究では,4次元の場合に具体的な関係式を得たことで,高次元シンプレクティック多様体の構成的な研究の糸口を与えたといえる.また,力学系とシンプレクティック充填の観点からの接触多様体の特徴付けは,接触多様体の区別・分類に新たな視点を示唆するものである.

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Published: 2025-01-30  

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