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

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 $S^1$-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 $S^1$-manifolds with these fixed point data. Finally, we show that a certain multigraph behaves like a manifold.

References in corpus (1)

• Circle actions on almost complex manifolds with isolated fixed points

Cited by in corpus (4)

• Circle actions on four dimensional almost complex manifolds with discrete fixed point sets
• Circle actions on 6-dimensional oriented manifolds with 4 fixed points
• Circle actions on six dimensional oriented manifolds with isolated fixed points
• Circle actions on oriented manifolds with 3 fixed points