JournalsqtVol. 7 , No. 1pp. 29–105

Lifting pseudo-holomorphic polygons to the symplectisation of P×RP \times \mathbb{R} and applications

  • Georgios Dimitroglou Rizell

    University of Cambridge, UK
Lifting pseudo-holomorphic polygons to the symplectisation of $P \times \mathbb{R}$ and applications cover
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Abstract

Let R×(P×R)\mathbb R \times (P \times \mathbb R) be the symplectisation of the contactisation of an exact symplectic manifold PP, and let R×Λ\mathbb R \times \Lambda be a cylinder over a Legendrian submanifold of the contactisation. We show that a pseudo-holomorphic polygon in PP having boundary on the projection of Λ\Lambda can be lifted to a pseudo-holomorphic disc in the symplectisation having boundary on R×Λ\mathbb R \times \Lambda. 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 P×RP \times \mathbb{R} and applications. Quantum Topol. 7 (2016), no. 1 pp. 29–105

DOI 10.4171/QT/73