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Misha
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Let's consider CS functional for concreteness. The problem is that CS is neither Morse nor Morse-Bott (because its critical points are flat connections and character varieties of 3-manifold groups could be rather bad). The trick is to perturb CS to a Morse function. This was done first by Taubes ("Casson's invariant and gauge theory") and then developed into Floer theory.

Misha
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  • 163