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
Famous quotes containing the word handle:
“I believe that all the survivors are mad. One time or another their madness will explode. You cannot absorb that much madness and not be influenced by it. That is why the children of survivors are so tragic. I see them in school. They don’t know how to handle their parents. They see that their parents are traumatized: they scream and don’t react normally.”
—Elie Wiesel (b. 1928)