When Floer defined instanton Floer homology for an integer homology sphere. He chose a finite set of loops in the manifold and consider the holonomy along these loops as a perturbation on Chern-Simons functional. He proved we can choose the perturbation such that all irreducibles critical points of the perturbed CS functional are "non-degenerate" .

But his argument used the fact that the reducible flat connection over an integer homology sphere is isolated with the irreducible flat connections. So all irreducible flat connections modulo gauge transformation form a compact set.

For **rational homology** sphere, this may not be true. Can we still do holonomy perturbation to get this transverslity for irreducible critical points? How to control things near the reducible connections? (Of course, we can't define an Floer homology in this way.)