  We introduce a type of surgery decomposition of Weinstein manifolds we call
simplicial decompositions. The main result of this paper is that the
Chekanov-Eliashberg dg-algebra of the attaching spheres of a Weinstein manifold
satisfies a descent (cosheaf) property with respect to a simplicial
decomposition. Simplicial decompositions generalize the notion of Weinstein
connected sum and we show that there is a one-to-one correspondence (up to
Weinstein homotopy) between simplicial decompositions and so-called good
sectorial covers. As an application we explicitly compute the
Chekanov-Eliashberg dg-algebra of the Legendrian attaching spheres of a
plumbing of copies of cotangent bundles of spheres of dimension at least three
according to any plumbing quiver. We show by explicit computation that this
Chekanov-Eliashberg dg-algebra is quasi-isomorphic to the Ginzburg dg-algebra
of the plumbing quiver.
