Lagrangian Cobordisms in Liouville manifolds

TL;DR

This paper explores the use of stops in Liouville manifolds to analyze Lagrangian cobordisms and their role in the derived wrapped Fukaya category, including computations for non-compact Riemann surfaces.

Contribution

It introduces a stop-based framework for studying Lagrangian cobordisms in Liouville manifolds and computes cobordism groups for certain non-compact surfaces.

Findings

Use of stops elucidates Lagrangian cobordisms in Liouville manifolds.

Established exact triangles in the derived wrapped Fukaya category.

Computed cobordism groups for non-compact Riemann surfaces.

Abstract

Floer theory for Lagrangian cobordisms was developed by Biran and Cornea to study the triangulated structure of the derived Fukaya category of monotone symplectic manifolds. This paper explains how to use the language of stops to study Lagrangian cobordisms in Liouville manifolds and the associated exact triangles in the derived wrapped Fukaya category. Furthermore, we compute the cobordism groups of non-compact Riemann surfaces of finite type.