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.

Analytic Foundations

Many of these Floer homologies have not been completely rigorously constructed, and many conjectural equivalences have not been proving, due to the difficulty of the analysis involved, especially in constructing compactification moduli spaces of pseudoholomorphic curves. Hofer, in collaboration with Kris Wysocki and Eduard Zehnder, has developed new analytic foundations via their theory of polyfolds. A preliminary version of the first volume (of four) of their book on their theory was circulated in 2005.

Related Topics:
Compactification - Moduli space - Pseudoholomorphic curves - Polyfolds

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