  This is a noncommutative-geometric study of the semiclassical dynamics of
finite topological D-brane systems. Starting from the formulation in terms of A
-infinity categories, I show that such systems can be described by the
noncommutative symplectic supergeometry of Z2-graded quivers, and give a
synthetic formulation of the boundary part of the generalized WDVV equations.
In particular, a faithful generating function for integrated correlators on the
disk can be constructed as a linear combination of quiver necklaces, i.e. a
function on the noncommutative symplectic superspace defined by the quiver's
path algebra. This point of view allows one to construct extended moduli spaces
of topological D-brane systems as non-commutative algebraic `superschemes'.
They arise by imposing further relations on a Z2-graded version of the quiver's
preprojective algebra, and passing to the subalgebra preserved by a natural
group of symmetries.
