TiTle:  Simple homotopy theory for Fukaya categories

Abstract:  We introduce a categorical framework for simple homotopy theory in Fukaya categories, based on the fundamental group of the ambient symplectic manifold. As a consequence, we prove that any two closed exact Lagrangians that are isomorphic in the Fukaya category of a Weinstein manifold are simple homotopy equivalent, under the assumption that one of them is homotopy equivalent to the ambient symplectic manifold. This generalizes Abouzaid-Kragh's result for cotangent bundles to general Weinstein manifolds.