Circle actions on almost complex manifolds with isolated fixed points

Abstract

The author proved that if the circle acts symplectically on a compact, connected symplectic manifold $M$ with three fixed points, then $M$ is equivariantly symplectomorphic to some standard action on ${\mathbb{CP}}^2$. In this paper, we extend the result to a circle action on an almost complex manifold; if the circle acts on a compact, connected almost complex manifold $M$ with exactly three fixed points, then $\dim M=4$. Moreover, we deal with the cases of one fixed point and two fixed points.

References in corpus (2)

• Hamiltonian circle actions on eight dimensional manifolds with minimal fixed sets
• Symplectic circle actions with isolated fixed points

Cited by in corpus (11)

• 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
• Circle actions on unitary manifolds with discrete fixed point sets
• Non-Hamiltonian actions with fewer isolated fixed points
• Circle actions on four dimensional almost complex manifolds with discrete fixed point sets
• On circle actions with exactly three fixed points
• Circle actions on 6-dimensional oriented manifolds with 4 fixed points
• A proof of Kosniowski conjecture
• Circle actions on oriented manifolds with 3 fixed points
• Kosniowski's conjecture and weights