Floer Homology

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Floer homology is typically defined by associating an infinite dimensional manifold to the object of interest. In the symplectic version, this is the free loop space of a symplectic manifold, while in the three-dimensional manifold version, it is the space of SU(2)-connections on a three-dimensional manifold. Loosely speaking, Floer homology is the Morse homology computed from a natural function on this infinite dimensional manifold. This function is the symplectic action on the free loop space or the Chernâ€“Simons function on the space of connections. A homology theory is formed from the vector space spanned by the critical points of this function. A...

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