For questions about Morse theory, which is a branch of differential topology to analyze topology of manifolds by studying differentiable functions on them.

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.

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