In mathematics, a handle decomposition of an m-manifold M is a union
where each is obtained from by the attaching of -handles. A handle decomposition is to a manifold what a CW-decomposition is to a topological space—in many regards the purpose of a handle decomposition is to have a language analogous to CW-complexes, but adapted to the world of smooth manifolds. Thus an i-handle is the smooth analogue of an i-cell. Handle decompositions of manifolds arise naturally via Morse theory. The modification of handle structures is closely linked to Cerf theory.
Read more about Handle Decomposition: Motivation, Terminology, Cobordism Presentations, Morse Theoretic Viewpoint, Some Major Theorems and Observations
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