Deepening three-manifold theory

2014 Fiscal Year Final Research Report

• Project/Area Number: 22244004
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: KOJIMA Sadayoshi 東京工業大学, 情報理工学(系)研究科, 教授 (90117705)
• Co-Investigator(Kenkyū-buntansha): YOSHIDA Tomoyoshi 東京工業大学, 大学院理工学研究科, 教授 (60055324) ; KIN Eiko 東京工業大学, 大学院情報理工学研究科, 准教授 (80378554) ; TAKASAWA Mitsuhiko 東京工業大学, 大学院情報理工学研究科, 助教 (80323822) ; SAKASAI Takuya 東京工業大学, 大学院理工学研究科, 助教 (60451902) ; FUJIWARA Koji 東北大学, 大学院情報科学研究科, 教授 (60229078) ; UE Masaaki 京都大学, 大学院理学研究科, 教授 (80134443) ; ISHIKAWA Goo 北海道大学, 大学院理学研究科, 教授 (50176161) ; KAWASUMI Nariya 東京大学, 大学院数理科学研究科, 准教授 (30214646)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: ３次元トポロジー / 幾何構造 / 位相不変量 / 計算機支援 / 体積 / ２次特性類 / 力学系 / 葉層構造

Outline of Final Research Achievements

Based on the role of genus in surface topology, we planned to develop the 3-manifold topology by bridging three concepts, geometric structures, topological invariants and computing，and to obtain fundamental results on several topics which are supposed to appear in the standard textbooks of 3-manifold theory in 10 years. We then have obtained in the last 5 years a few fundamental results on the geometric structures and geometric group theory, on the invariants coming from 1 or 2 dimensional objects and on computational topology. Among them, the comparison study for entropy of surface automorphisms and simplicial volume of their maping tori could be featured.

Free Research Field

幾何学・トポロジー