Circle actions on oriented manifolds with discrete fixed point sets and classification in dimension 4
Differential Geometry
2019-04-05 v3
Abstract
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 of the -representations 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 oriented -manifolds with these fixed point data. Finally, we show that a certain multigraph behaves like a manifold.
Cite
@article{arxiv.1703.05464,
title = {Circle actions on oriented manifolds with discrete fixed point sets and classification in dimension 4},
author = {Donghoon Jang},
journal= {arXiv preprint arXiv:1703.05464},
year = {2019}
}