Symplectic Geometry Seminar

In this talk, we will present a proof of contact big fiber theorem, based on invariants read off from contact Hamiltonian Floer homology. The theorem concludes that any contact involutive map on a Liouville fillable contact manifold admits at least one fiber that is non-displaceable, under the condition that the Liouville filling has non-vanishing symplectic homology. Note that this result was also proved recently by Sun-Uljarevic-Varolgunes, based on symplectic homology with compact support. Along with the proof, we will also propose a definition of partial contact quasi-state (and contact quasi-measure), serving as a contact analog to Entov-Polterovich’s quasi-state machinery in the symplectic setting. This talk is based on joint work with Igor Uljarevic.