Topology of stable mappings and diagrams of four-manifolds

2017 Fiscal Year Final Research Report

• Project/Area Number: 26800027
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Keio University (2016-2017); Hokkaido University (2014-2015)
• Principal Investigator: Hayano Kenta 慶應義塾大学, 理工学部(矢上), 講師 (20722606)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 安定写像 / 写像類群 / 消滅サイクル / trisection

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.

Free Research Field

低次元トポロジー