On partially wrapped Fukaya categories

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 ∞ -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.