Linked from

The 10 pages that link to Morse theory, each with the reason it gives.

• Level setRelated: Changes in level-set topology occur as the value crosses critical values.

• Differential topologyRelated: It converts the derivative data of functions into information about manifold topology.

• Poincaré–Hopf theoremRelated: For gradient fields, the theorem recovers the alternating critical-point count in Morse theory.

• Saddle pointRelated: The number of descending directions at a saddle contributes to its Morse index.

• John MilnorRelated: Milnor’s textbook and research clarified how critical points reveal manifold topology.

• Sylvester's law of inertiaRelated: The Hessian's negative count gives the Morse index used to track topology.

• Differentiable manifoldRelated: Smooth functions reveal topological information through their critical points.

• Sard's theoremRelated: Sard's theorem supplies regular levels between critical values.

• Cell (topology)Related: Morse theory often builds a space by adding one cell at each critical point.

• Lefschetz hyperplane theoremRelated: The proof builds the variety from the section using cells constrained by Morse indices.