Lifting pseudo-holomorphic polygons to the symplectisation of and applications

  • Georgios Dimitroglou Rizell

    University of Cambridge, UK

Abstract

Let be the symplectisation of the contactisation of an exact symplectic manifold , and let be a cylinder over a Legendrian submanifold of the contactisation. We show that a pseudo-holomorphic polygon in having boundary on the projection of can be lifted to a pseudo-holomorphic disc in the symplectisation having boundary on . 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.

Cite this article

Georgios Dimitroglou Rizell, Lifting pseudo-holomorphic polygons to the symplectisation of and applications. Quantum Topol. 7 (2016), no. 1, pp. 29–105

DOI 10.4171/QT/73