Yaniv Ganor (Holon Institute of Technology)
Abstract: Poisson bracket invariants, introduced by Buhovsky, Entov, and Polterovich, are symplectic invariants of quadruples of closed sets whose nonvanishing implies the existence of Hamiltonian trajectories between the sets, with an explicit time-length bound. In this talk, we establish lower bounds on these invariants for certain configurations in completions of Liouville manifolds, expressed in terms of the barcode of wrapped Floer homology. This is inspired by a work of Entov and Polterovich, who obtained analogous results for Lagrangian cobordisms between Legendrians using persistence in Legendrian contact homology. Our main examples concern cotangent bundles, where the quadruple consists of two cosphere bundles of different radii and two cotangent fibers over distinct points, yielding concrete bounds on Hamiltonian trajectories related to perturbed geodesic flows.