UC Berkeley

We define a new class of symplectic spaces called ``pumpkin domains'', which roughly speaking comprise a Liouville domain and a Liouville hypersurface of its boundary. To such an object we assign an $A_\infty$-category called its partially wrapped Fukaya category. An exact Landau-Ginzburg model gives rise to a pumpkin domain, and the partially wrapped Fukaya category of this pumpkin domain 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 the partially wrapped Fukaya category of a pumpkin domain to the wrapped Fukaya category of its underlying Liouville domain. This operation is mirror to removing a divisor.