Donghoon Jang, Circle Actions on Almost Complex Manifolds with Isolated Fixed Points

We briefly review group actions on manifolds and equivariant cohomology, which is cohomology of a manifold with a group action. We review classification results for circle actions on various types of manifolds in low dimensions. An almost complex manifold is a manifold with a complex structure on its tangent bundle; every complex or symplectic manifold is almost complex. For an action of the circle group on a compact almost complex manifold that has isolated fixed points, we study its properties and discuss the classification when the number of fixed points is small.