We relate the cluster theory of an arbitrary quiver to the
symplectic geometry of a corresponding exact symplectic 4-manifold.
The symplectic manifold is obtained from cotangent bundles of surfaces
by attaching Weinstein handles along Legendrians at infinity. The quiver is the
intersection graph of the projections of the Legendrians to the surface.

We prove that the cluster X-variety of the quiver is a moduli space of
rank one microlocal sheaves on a Lagrangian skeleton of the
4-manifold. In the resulting dictionary, cluster variables are named
by the Lagrangian disks at the cores of the handles, and mutation is
effected by Lagrangian disk surgery.

It is generally expected that the microlocal sheaf category on the
skeleton is equivalent to the Fukaya category of the symplectic
manifold. Assuming this holds, we are showing that a cluster variety
is a moduli space of Lagrangian branes inside a symplectic 4-manifold.