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In differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold.

4 votes

Is there a Morse theory for sections of bundles or more generally for maps?

There is some really cool recent work of Gay and Kirby on "Morse 2-functions", ie generic maps $f$ from an $n$-manifold $X$ to a surface $\Sigma$ (both compact, connected, oriented, smooth) (see http: …
Nathaniel Bottman's user avatar