  Generalizing our ideas in [arXiv:1006.3313], we explain how
topologically-twisted N=2 gauge theory on a four-manifold with boundary, will
allow us to furnish purely physical proofs of (i) the Atiyah-Floer conjecture,
(ii) Munoz's theorem relating quantum and instanton Floer cohomology, (iii)
their monopole counterparts, and (iv) their higher rank generalizations. In the
case where the boundary is a Seifert manifold, one can also relate its
instanton Floer homology to modules of an affine algebra via a 2d A-model with
target the based loop group. As an offshoot, we will be able to demonstrate an
action of the affine algebra on the quantum cohomology of the moduli space of
flat connections on a Riemann surface, as well as derive the Verlinde formula.
