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:
“If there is a species which is more maltreated than children, then it must be their toys, which they handle in an incredibly off-hand manner.... Toys are thus the end point in that long chain in which all the conditions of despotic high-handedness are in play which enchain beings one to another, from one species to another—cruel divinities to their sacrificial victims, from masters to slaves, from adults to children, and from children to their objects.”
—Jean Baudrillard (b. 1929)