Study of stability of fixed point sets in equivariant manifolds

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400090
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Okayama University
• Principal Investigator: MORIMOTO Masaharu 岡山大学, 自然科学研究科, 教授 (30166441)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 同変多様体 / 変換群論 / 不動点集合 / 同変手術理論 / 同変コボルディズム

Outline of Final Research Achievements

Let G be a finite group and let F be a closed manifold satisfying a certain condition such as one of G-fixed point sets of smooth G-actions on disks or spheres. The purpose of this research project was to construct smooth G-actions with fixed point set F on a specified sequence X(1), X(2), X(3), ... of closed manifolds X(n), for example complex projective spaces, real projective spaces, and lens spaces. In the period of the present research project, we constructed smooth G-actions with fixed point set F for the group G being the alternating group of degree 5 or 6, on sequences of complex projective spaces, real projective spaces, and lens spaces, by means of the reflection method of G-framed maps and equivariant cobordisms, equivariant surgery theory, and s-cobordism theory.

Free Research Field

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