Hamiltonian circle actions with almost minimal isolated fixed points

JOURNAL OF GEOMETRY AND PHYSICS

卷:163

Article

Li, Hui¹ 

[1] Soochow Univ, Sch Math Sci, Suzhou 215006, Peoples R China

关键词: Symplectic manifold;    Hamiltonian circle action;    Equivariant cohomology;    Chern classes;    Kahler manifold;    Symplectomorphism;   

DOI  :  10.1016/j.geomphys.2021.104141

来源: Elsevier

【 摘 要 】

Let the circle act in a Hamiltonian fashion on a connected compact symplectic manifold (M , omega) of dimension 2 pi. Then the S-1-action has at least n + 1 fixed points. In a previous paper, we study the case when the fixed point set consists of precisely n + 1 isolated points. In this paper, we study the case when the fixed point set consists of exactly n+2 isolated points. We show that in this case n must be even. We find equivalent conditions on the first Chern class of M and a particular weight of the S-1-action. We also show that the particular weight can completely determine the integral cohomology ring and the total Chern class of M , and the sets of weights of the S-1-action at all the fixed points. (G) over tilde (2)(Rn+2) with n >= 2 even, equipped with standard circle actions. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free