  This paper studies geometric engineering, in the simplest possible case of
rank one (Abelian) gauge theory on the affine plane and the resolved conifold.
We recall the identification between Nekrasov's partition function and a
version of refined Donaldson-Thomas theory, and study the relationship between
the underlying vector spaces. Using a purity result, we identify the vector
space underlying refined Donaldson-Thomas theory on the conifold geometry as
the exterior space of the space of polynomial functions on the affine plane,
with the (Lefschetz) SL(2)-action on the threefold side being dual to the
geometric SL(2)-action on the affine plane. We suggest that the exterior space
should be a module for the (explicitly not yet known) cohomological Hall
algebra (algebra of BPS states) of the conifold.
