Partially wrapped contact Fukaya categories of 1-jet spaces

Abstract

We introduce the partially wrapped contact Fukaya category of a 1-jet space equipped with a stop, which is an \(A_\infty\)-category of Legendrians equipped with representations of their Chekanov-Eliashberg algebras. This category is invariant under contact isotopies of the stop. We prove a wrapping exact triangle and a generation theorem. When the stop is bounded subanalytic singular isotropic, we prove a Morita equivalence between the partially wrapped contact Fukaya category and a microlocal sheaf category.