On the classification of quasitoric manifolds

2021 Fiscal Year Final Research Report

• Project/Area Number: 18K13414
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 11020:Geometry-related
• Research Institution: Osaka Prefecture University (2021); University of Tsukuba (2018-2020)
• Principal Investigator: Hasui Sho 大阪府立大学, 理学(系)研究科(研究院), 准教授 (50792454)
• Project Period (FY): 2018-04-01 – 2022-03-31
• Keywords: 擬トーリック多様体 / トーリックトポロジー / 代数的位相幾何学

Outline of Final Research Achievements

The subject of this research is to study the classification of quasitoric manifolds. With the idea, posed in the research plan, that we can construct some non-equivariant homeomorphisms between quasitoric manifolds by cutting the quotient polytope, I obtained some foundational results, which support some known classification results in a different direction.
On the other hand, as another approach to this kind of manifolds, I studied the moment-angle manifolds and their quotient manifolds, which include the quasitoric manifolds, from the viewpoint of characteristic classes, and obtained some new results. Those results have already been made up into a manuscript and submitted to a journal.

Free Research Field

代数的位相幾何学

Academic Significance and Societal Importance of the Research Achievements

トーリックトポロジーは位相幾何学、代数幾何学、組み合わせ論などの諸分野の交差的領域であり、今回成果を得た対象である擬トーリック多様体とモーメント・アングル複体は組み合わせ的幾何学と位相幾何学の橋渡しをする位置にある。擬トーリック多様体に関する成果は組み合わせ的情報のトポロジーへの反映をより柔軟に捉えるための基礎となりうるものであり、モーメント・アングル複体についても特性類の観点からこれまであまり省みられていなかった部分に光を当てることができた。