: Mathématiques: Floer homology

topology > algebraic topology > homology > Floer homology

mathematical physics > dynamical systems theory > dynamical system > Floer homology

geometry > differential geometry > symplectic geometry > Floer homology

Floer homology

In mathematics, Floer homology is a tool for studying symplectic geometry and low-dimensional topology. Floer homology is a novel invariant that arises as an infinite-dimensional analogue of finite-dimensional Morse homology. Andreas Floer introduced the first version of Floer homology, now called Lagrangian Floer homology, in his proof of the Arnold conjecture in symplectic geometry. Floer also developed a closely related theory for Lagrangian submanifolds of a symplectic manifold. A third construction, also due to Floer, associates homology groups to closed three-dimensional manifolds using the Yang–Mills functional. These constructions and their descendants play a fundamental role in current investigations into the topology of symplectic and contact manifolds as well as (smooth) three- and four-dimensional manifolds.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Floer_homology)

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