Hamiltonian no-torsion

Abstract: We generalize in several ways Polterovich's well-known theorem that the Hamiltonian group of a closed symplectically aspherical manifold admits no non-trivial elements of finite order. We prove an analogous statement for Calabi-Yau and negatively monotone manifolds. For positively monotone manifolds we prove that non-trivial torsion implies geometric uniruledness of the manifold, answering a question of McDuff-Salamon. Moreover, in this case the following symplectic Newman theorem holds: a small Hofer-ball around the identity contains no finite subgroup. This is joint work with Marcelo Atallah.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

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