Abstract
Assume that we are given a closed chord-generic Legendrian sub-manifold Lambda subset of P x R of the contactisation of a Liouville manifold, where Lambda moreover admits an exact Lagrangian filling L-Lambda subset of R x P x R inside the symplectisation. Under the further assumptions that this filling is spin and has vanishing Maslov class, we prove that the number of Reeb chords on Lambda is bounded from below by the stable Morse number of L-Lambda.
Given a general exact Lagrangian filling L-Lambda, we show that the number of Reeb chords is bounded from below by a quantity depending on the homotopy type of L-Lambda, following Ono-Pajitnov's implementation in Floer homology of invariants due to Sharko. This improves previously known bounds in terms of the Betti numbers of either Lambda or L-Lambda.