Classification of Hamiltonian Circle Actions on Compact Symplectic Orbifolds of Dimension Four

Speaker: Grace Mwakyoma, IST Lisboa - IMPA.

Date: 16 aug 2019, 11h.

Place: Room 407, Bloco H, Campus Gragoatá, UFF.

Abstract: Circle actions have attracted much recent attention in geometry and topology. In the terminology of dynamical systems, they are regarded as periodic flows and their fixed points correspond to equilibrium points.

A complete classification of Hamiltonian circle actions on compact manifolds of dimension four was obtained by Y. Karshon, following the work of M. Audin and K. Ahara and A. Hattori. In particular, it was shown that all these spaces are Kahler, that every example can be obtained from a simple model by a sequence of symplectic blowups and, if the fixed points are isolated, the circle actions extend to toric actions. In higher dimensions much less is known. There are however some partial classification results.

The present research aims at completely classifying Hamiltonian circle actions on compact orbifolds of dimension 4 when the fixed points are isolated. These spaces appear, for example, as reduced spaces of Hamiltonian torus actions at regular level sets of the moment map where the action is not free. L. Godinho shows in her classification of semifree Hamiltonian circle actions on compact 4-orbifolds that the situation is much different from the manifold case. For example, these actions can have any number of fixed points while, in the manifold case, they have exactly four fixed points.