Topological studies on mapping class groups of knotted surafces and 3-dimensional handlebodies

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540096
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Tokyo University of Science
• Principal Investigator: Hirose Susumu 東京理科大学, 理工学部, 教授 (10264144)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 位相幾何学 / 低次元トポロジー / 写像類群 / 曲面結び目 / ３次元ハンドル体

Outline of Final Research Achievements

We made several researches mainly on the mapping class group related to topology on the surface embedded in 3 or 4-manifolds. Especially, we obtained results on the abelianization and minimal generating set of the level 2 mapping class groups of non-orientable surfaces, a normal generating set of the Torelli groups of non-orientable surfaces, pseudo-Anosov elements and finite presentations of the hyper-elliptic handlebody group, links which are closed orbits of Morse-Smale flows on the 3-sphere, a uniqueness and periods of null-cobordant periodic maps on closed orientable surfaces, and a uniqueness of periodic maps on compact surfaces with boundaries.

Free Research Field

数物系科学