THE GROUP ACTIONS ON MANIFOLDS AND THE EQUIVARIANT DETERMINANT OF ELLIPTIC OPERATORS.

2017 Fiscal Year Final Research Report

• Project/Area Number: 25400084
• 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 Marine Science and Technology
• Principal Investigator: TSUBOI KENJI 東京海洋大学, 学術研究院, 教授 (50180047)
• Project Period (FY): 2013-04-01 – 2018-03-31
• Keywords: 概複素多様体 / 向き付けられた多様体 / 有限群作用 / 楕円型作用素 / 同変行列式

Outline of Final Research Achievements

Firstly we obtain a necessary condition for the existence of finite group actions on alomost complex manifolds, where the action is assumed to preserve the almost complex structure and the fixed points of the action is assumed to be isolated. The condition above contains the condition of Harvey for compact Riemann surfaces. This result is published in J.Math.Soc.Japan, vol.65-3, p.797-827 at June, 2013. Secondly we show that the C-p groups can act on Riemann surfaces of genus r for some p,r, where C-p group is a finite group such that the order of the commutator subgroup is a multiple of the prime number p. Thirdly we obtain a necessary condition for the existence of finite group actions on oriented manifolds, where the action is assumed to preserve the orientation and the fixed points of the action is assumed to be isolated. The condition above contains the condition of Harvey for compact Riemann surfaces.

Free Research Field

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