Let $Y$ be a $3$-manifold. Suppose that $P \rightarrow Y$ is a principle $SU(2)$-bundle with a choice of trivialization. Then the space of connections over $P$ is identified with $1$-forms taking value in $\mathfrak{su}(2)$. Let $A \in \Omega_{Y}^{1}(\mathfrak{su}(2))$ be a connection, then the Chern-Simons functional is defined by $CS(A) = \int_{Y} tr(A \wedge dA + \frac23 A \wedge A \wedge A)$.

To define Floer theory, people always perturb the Chern-Simons functional by holonomy perturbations, originating from Donaldson and Floer. The perturbation space is usually "abundant" and the compactness arguments go through without much change.

But from the viewpoint of equivariant Morse homology, there should be a larger class of perturbations of the Chern-Simons functional which result in a construction of (equivariant) Floer homology. So the question is: are there any other effective ways to perturb $CS$?


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