Circle actions on oriented manifolds with discrete fixed point sets and classification in dimension 4

JOURNAL OF GEOMETRY AND PHYSICS

卷:133

Article

Jang, Donghoon¹ 

[1] Pusan Natl Univ, Dept Math, Pusan 46241, South Korea

关键词: Circle action;    Oriented manifold;    Fixed point;    Weight;   

DOI  :  10.1016/j.geomphys.2018.07.010

来源: Elsevier

【 摘 要 】

In this paper, we study a circle action on a compact oriented manifold with a discrete fixed point set. The fixed point data consists of the weights at the fixed points. We prove various results and properties of the action, in terms of the fixed point data. We show that the manifold can be described by a multigraph associated to it. Specializing into the case of dimension 4, we classify the fixed point data. Moreover, we prove that there exist circle actions on oriented manifolds with these fixed point data. Finally, we show that a certain multigraph behaves like a manifold. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free