AbstractFloer defined Floer homology in two different cases. One is the case of Instanton Floer homology of 3 manifolds (homology sphere). The other uses pseudo-holomorphic curves. (The first Floer homology Floer defined using pseudo-holomorphic curves is Lagrangian Floer homology.) Atiyah-Floer conjecture says that those two coincide in certain situations. This is > 30 year old conjecture. I w...
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