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

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 ${\mathbb{C}\mathbb{P}}^3$. The former case includes that of Petrie’s exotic action on ${\mathbb{C}\mathbb{P}}^3$.