Appears in collection : 2021 - T2 - Symplectic topology, contact topology and interactions
Joint work with G. Dimitroglou-Rizell and P. Ghiggini.
Let L be a compact Lagrangian in a Weinstein manifold obtained from a subcritical one by attaching a handle along a Legendrian V. We will see how to associate to L a filling of a satelite of V and how this one induces a representation of the Chekanov-Eliashberg algebra of V. We will show that Legendrian contact homology linearised with respect to this representation recovers the Floer homology of L. We will talk about extensions of this considerations to A-infinity opérations on both sides.