Editing Morse theory (section)

===Morse homology===
[[Morse homology]] is a particularly easy way to understand the [[Homology (mathematics)|homology]] of [[smooth manifold]]s. It is defined using a generic choice of Morse function and [[Riemannian metric]].  The basic theorem is that the resulting homology is an invariant of the manifold (that is, independent of the function and metric) and isomorphic to the singular homology of the manifold; this implies that the Morse and singular [[Betti number]]s agree and gives an immediate proof of the Morse inequalities.  An infinite dimensional analog of Morse homology in [[symplectic geometry]] is known as [[Floer homology]].