Circle actions on four dimensional almost complex manifolds with discrete fixed point sets

Abstract

We establish a necessary and sufficient condition for pairs of integers to arise as the weights at the fixed points of an effective circle action on a compact almost complex 4-manifold with a discrete fixed point set. As an application, we provide a necessary and sufficient condition for a pair of integers to arise as the Chern numbers of such an action, answering negatively a question by Sabatini whether $c_1^2[M]\le 3c_2[M]$ holds for any such manifold $M$. We achieve this by demonstrating that pairs of integers that arise as weights of a circle action, also arise as weights of a restriction of a ${\mathbb{T}}^2$-action. Furthermore, we discuss applications to circle actions on complex/symplectic 4-manifolds and semi-free circle actions with discrete fixed point sets.

Major revision. Readability improved

References in corpus (5)

• Circle actions on almost complex manifolds with isolated fixed points
• Hamiltonian circle actions on eight dimensional manifolds with minimal fixed sets
• Circle actions on almost complex manifolds with 4 fixed points
• Symplectic circle actions with isolated fixed points
• Circle actions on oriented manifolds with discrete fixed point sets and classification in dimension 4

Cited by in corpus (2)

• Circle actions on unitary manifolds with discrete fixed point sets
• Circle actions on six dimensional oriented manifolds with isolated fixed points