Morse theory

"Morse function" redirects here. In another context, a "Morse function" can also mean an anharmonic oscillator: see Morse potential.

In differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold. According to the basic insights of Marston Morse, a typical differentiable function on a manifold will reflect the topology quite directly. Morse theory allows one to find CW structures and handle decompositions on manifolds and to obtain substantial information about their homology.