Floer homology

In mathematics, Floer homology refers to a family of homology theories which share similar characteristics and are believed by experts to be closely related. Some of these theories are due directly to Andreas Floer, while others are derived or inspired by his work. They are all modelled upon Morse homology on finite dimensional manifolds, extending it to the case where the relevant Morse function has finite relative indices. The differentials all count some sort of pseudoholomorphic curves.

Heegaard Floer Homology

Heegaard Floer Homology is an invariant of a closed 3-manifold equipped with a spin^c structure. It is computed using a Heegaard diagram of the space via Lagrangian Floer homology. It is conjecturally equivalent to Seiberg-Witten-Floer homology. A knot in a three-manifold induces a filtration on the homology groups, and the filtered homotopy type is a powerful knot invariant which dominates the Alexander polynomial.

Related Topics:
Spin^c structure - Heegaard diagram

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