Flexibilities of finite group actions on manifolds

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540083
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Kyushu University
• Principal Investigator: SUMI Toshio 九州大学, 基幹教育院, 准教授 (50258513)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 有限群作用 / スミス集合 / 実表現

Outline of Final Research Achievements

I studied representation spaces induced by smooth actions on manifolds of finite groups. In particular, I studied finite group smooth actions on spheres. The Smith problem, whether tangential representation spaces over fixed points of a sphere with just two fixed points are isomorphic?, is fundamental one for transformation group theory. I determinied the Smith set which consists of the differences of tangential representative spaces over such a sphere for some class of finite groups. I also gave a sufficient and necessary condition for a finite group to be a gap group by viewing centralizers and normalizers.

Free Research Field

変換群論