Circle actions on 6-dimensional oriented manifolds with 4 fixed points

Abstract

In this paper, we classify the fixed point data (weights and signs at the fixed points), of a circle action on a 6-dimensional compact oriented manifold with 4 fixed points. We prove that it agrees with that of a disjoint union of rotations on two 6-spheres, or that of a linear action on ${\mathbb{CP}}^3$. The former case includes that of Petrie's exotic action on ${\mathbb{CP}}^3$.

References in corpus (4)

• Circle actions on almost complex manifolds with isolated fixed points
• Circle actions on almost complex manifolds with 4 fixed points
• Circle actions on oriented manifolds with discrete fixed point sets and classification in dimension 4
• Circle actions on 8-dimensional almost complex manifolds with 4 fixed points