researchseminars.org

Egor Shelukhin (University of Montreal)
2021-11-03 14:10 - 15:30 UTC | https://researchseminars.org/talk/GDS/39/
Title: Hamiltonian no-torsion (https://researchseminars.org/talk/GDS/39/)
by Egor Shelukhin (University of Montreal) as part of Geometry and Dynamics seminar

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.
