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T&G: Liat Kessler (Cornell and Oranim), Extending Homologically trivial symplectic cyclic actions to Hamiltonian circle actions | Einstein Institute of Mathematics

T&G: Liat Kessler (Cornell and Oranim), Extending Homologically trivial symplectic cyclic actions to Hamiltonian circle actions

Date: 
Tue, 12/09/201712:00-13:00
Location: 
Ross Building Room 70A
We ask whether every homologically trivial cyclic action on a symplectic four-manifold extend to a Hamiltonian circle action. By a cyclic action we mean an action of a cyclic group of finite order; it is homologically trivial if it induces the identity map on homology. We assume that the manifold is closed and connected. In the talk, I will give an example of a homologically trivial symplectic cyclic action on a four-manifold that admits Hamiltonian circle actions, and show that is does not extend to a Hamiltonian circle action. I will also discuss symplectic four-manifolds on which every homologically trivial cyclic action extends to a Hamiltonian circle action. I will deduce corollaries on the existence of homologically trivial cyclic actions and on embedding finite-order cyclic subgroups of the group of Hamiltonian symplectomorphisms in circle subgroups. This work applies holomorphic methods to extend combinatorial tools developed for circle actions to study cyclic actions.