Study of Foliations and Group Actions

2023 Fiscal Year Final Research Report

• Project/Area Number: 18K03312
• 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: Nihon University
• Principal Investigator: MATSUMOTO Shigenori 日本大学, 理工学部, 名誉教授 (80060143)
• Co-Investigator(Kenkyū-buntansha): 平田 典子 (河野典子) 日本大学, 理工学部, 特任教授 (90215195) ; 西川 貴雄 日本大学, 理工学部, 准教授 (10386005)
• Project Period (FY): 2018-04-01 – 2024-03-31
• Keywords: 葉層構造

Outline of Final Research Achievements

Let S be a closed oriented surface of negative Euler number, and let M be the unit tangent bundle of S. The orientable infinitely differentiable codimension one foliations on M are mutually topologically equivalent. Choose two such foliations and assume they are mutually transverse. The typical examples of such intersections is obtained by the stable and unstable foliations of the geodesic flow. But there are other transverse intersections. We investigate such intersections.

Free Research Field

数学（位相幾何学）

Academic Significance and Societal Importance of the Research Achievements

3次元多様体上の余次元１葉層構造自体は様々な角度から調べられている。しかし二つの葉層構造の横断的交わりを詳しく調べる研究はかつてなされていなかった。我々に構成した葉層構造の交わりは、かなり不思議なものであり、一般に想像されるものとはかなり趣を異にしている。