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

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 describe...

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Bibliographic Details
Published in:Journal of geometry and physics 2018-11, Vol.133, p.181-194
Main Author: Jang, Donghoon
Format: Article
Language:English
Subjects:
Circle action
Fixed point
Oriented manifold
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Summary: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.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2018.07.010