Invariants of low dimensional manifolds from infinite dimensional dynamics in gauge theory and homotopy theory

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K03493
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 11020:Geometry-related
• Research Institution: Kyushu University
• Principal Investigator: Sasahira Hirofumi 九州大学, 数理学研究院, 教授 (30466825)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Keywords: Seiberg-Witten理論 / Floer理論

Outline of Final Research Achievements

I studied the Seiberg-Witten Floer stable homotopy type which is an invariant of closed 3-manifolds. The invariant had been defined only for 3-manifolds with first Betti number zero and computed only for a few types of Seifert fibered spaces. I have studied to extend the invariant to a class of 3-manifolds and to establish a way to compute for more 3-manifolds.

Free Research Field

幾何学

Academic Significance and Societal Importance of the Research Achievements

シンプレクティック幾何学や結び目理論などに関するFloer理論では、ホモロジー的不変量からホモトピー的不変量への精密化が盛んに研究され、成果が出つつある。本研究ではSeiberg-Witten Floer理論において、その研究の流れを進めることができた。