Topology related with surfaces and 3-mainfolds

2017 Fiscal Year Final Research Report

• Project/Area Number: 15H03619
• Research Category: Grant-in-Aid for Scientific Research (B)
• 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, 情報理工学院, 教授 (90117705)
• Co-Investigator(Kenkyū-buntansha): 藤原 耕二 京都大学, 理学研究科, 教授 (60229078) ; 逆井 卓也 東京大学, 数理(科)学研究科(研究院), その他 (60451902) ; 高澤 光彦 東京工業大学, 情報理工学院, 助教 (80323822)
• Project Period (FY): 2015-04-01 – 2018-03-31
• 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

Outline of Final Research Achievements

The surface theory and the theory of 3-manifold are linked each other. The aim of this study is to deepen understandings between them especially on invariants of mapping classes, separability of subgroups and computing in topology. In particular, we would have liked to develop comparisons of invariants of mapping classes which do not depend on the topology of surfaces. We then have proved that the normalized entropy of a pseudo-Anosov over the volume of its mapping torus is uniformly bounded from below by some explicit positive constant.

Free Research Field

トポロジー