Extending cyclic actions to circle actions

Abstract: It is natural to ask whether an action of a finite cyclic group extends to a circle action. Here, the action is on a symplectic manifold of dimension four. Admitting a circle action implies that a simply connected closed symplectic four-manifold is either the projective plane or obtained from an $S^2$ bundle over $S^2$ by k blowups. I will show that for k small enough, any cyclic action that is trivial on homology extends to a circle action, and present a case in which the action does not extend. I will also discuss how we approach this question for a general k. The proofs combine holomorphic and combinatorial methods. The talk is based on a joint work with River Chiang.

algebraic geometrydifferential geometrysymplectic geometry

Audience: researchers in the topic

Geometria em Lisboa (IST)

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