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

TL;DR

This paper constructs an $A_ abla$-category for exact Lagrangian cobordisms in symplectizations, utilizing Floer complexes derived from Symplectic Field Theory to encode morphisms.

Contribution

It introduces a new unital $A_ abla$-category framework for Lagrangian cobordisms using Rabinowitz Floer complexes within SFT.

Findings

Defines a unital $A_ abla$-category for Lagrangian cobordisms

Uses Floer complexes based on Rabinowitz Floer theory

Provides a new categorical perspective in symplectic topology

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.