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- Q2296951 subject Q10000447.
- Q2296951 subject Q7009992.
- Q2296951 subject Q7110104.
- Q2296951 abstract ""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.Before Morse, Arthur Cayley and James Clerk Maxwell had developed some of the ideas of Morse theory in the context of topography. Morse originally applied his theory to geodesics (critical points of the energy functional on paths). These techniques were used in Raoul Bott's proof of his periodicity theorem.The analogue of Morse theory for complex manifolds is Picard–Lefschetz theory.".
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- Q2296951 comment ""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.".
- Q2296951 label "Morse theory".
- Q2296951 depiction Saddle_point.png.