A-infinity category of Lagrangian cobordisms in the symplectization of PxR

Abstract

We define a unital $A_\infty$-category whose objects are exact Lagrangian cobordisms in the symplectization of $Y=P\times\mathbb{R}$, with negative cylindrical ends over Legendrians equipped with augmentations. The morphism spaces are given in terms of Floer complexes $Cth_+(\Sigma_0,\Sigma_1)$ which are versions of the Rabinowitz Floer complex defined by Symplectic Field Theory (SFT) techniques.