Lifting pseudo-holomorphic polygons to the symplectisation of P × R and applications

الأصل · EN

Let R × (P × R) be the symplectisation of the contactisation of an exact symplectic manifold P, and let R × Λ be a cylinder over a Legendrian submanifold in the contactisation. We show that a pseudo-holomorphic polygon in P having boundary on the projection of Λ can be lifted to a pseudo-holomorphic disc in the symplectisation having boundary on R × Λ. It follows that Legendrian contact homology may be equivalently defined by counting either of these objects. Using this result, we give a proof of Seidel's isomorphism of the linearised Legendrian contact homology induced by an exact Lagrangian filling and the singular homology of the filling.