On partially wrapped Fukaya categories

TL;DR

This paper introduces 'stops' in Liouville domains to define partially wrapped Fukaya categories, linking symplectic geometry with Landau-Ginzburg models and providing new tools like cascade-free continuation functors.

Contribution

It defines a new class of symplectic objects called stops and constructs partially wrapped Fukaya categories, connecting them to Landau-Ginzburg models and wrapped Fukaya categories.

Findings

Relation between partially wrapped and wrapped Fukaya categories

Construction of cascade-free continuation functors

Framework for associating Fukaya categories to Landau-Ginzburg models

Abstract

We define a new class of symplectic objects called "stops", which roughly speaking are Liouville hypersurfaces in the boundary of a Liouville domain. Locally, these can be viewed as pages of a compatible open book. To a Liouville domain with a collection of disjoint stops, we assign an $A_\infty$-category called its partially wrapped Fukaya category. An exact Landau-Ginzburg model gives rise to a stop, and the corresponding partially wrapped Fukaya category is meant to agree with the Fukaya category one is supposed to assign to the Landau-Ginzburg model. As evidence, we prove a formula that relates these partially wrapped Fukaya categories to the wrapped Fukaya category of the underlying Liouville domain. This operation is mirror to removing a divisor. In v2, we also construct continuation functors without cascades, which should be of independent interest.