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 $Ct{h}_{+}({\Sigma }_0,{\Sigma }_1)$ which are versions of the Rabinowitz Floer complex defined by Symplectic Field Theory (SFT) techniques.

77 pages, 27 figures. Completed proof of exactness of the Mayer-Vietoris sequence in Section 3.2.4 and first part of the proof of the Leibniz rule in Section 5.2. In Section 7: correction of a mistake in the definition of the continuation element and modification of the proofs of Proposition 10 and Theorem 6 accordingly. Accepted for publication in Quantum Topology

References in corpus (1)

• Covariantly functorial wrapped Floer theory on Liouville sectors