Roman Golovko: A few remarks on the Arnold's chord estimate

Given a chord-generic horizontally displaceable Legendrian submanifold L of the contactization of a Liouville manifold with the property that its Chekanov-Eliashberg algebra admits a finite-dimensional matrix representation, we prove that the number of Reeb chords on L is bounded from below by half of the Betti numbers of L. This bound is called the homological Arnold-type lower bound.
Moreover, if L admits an exact Lagrangian filling, we prove that the number of Reeb chords on L is bounded from below by the stable Morse number of the filling. In general, this bound is stronger than the homological Arnold-type lower bound. This is a joint work with Georgios Dimitroglou Rizell.