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.

Seiberg-Witten Floer homology

Seiberg-Witten Floer homology, also known as Monopole Floer homology is a homology theory of smooth 3-manifolds (equipped with a spin^c structure that is generated by solutions to Seiberg-Witten equations on a 3-manifold and whose differential counts invariant solutions to the Seiberg-Witten equations on the 3-manifold cross the real line.

Related Topics:
3-manifold - Spin^c structure

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SWF is constructed rigorously using finite-dimensional approximation in papers by Ciprian Manolescu and Manolescu and Peter Kronheimer; a more traditional approach is taken in the forthcoming book of Kronheimer and Tomasz Mrowka.

Related Topics:
Finite-dimensional approximation - Ciprian Manolescu - Peter Kronheimer - Kronheimer - Tomasz Mrowka

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