Local Operation
The connected sum is a local operation on manifolds, meaning that it alters the summands only in a neighborhood of . This implies, for example, that the sum can be carried out on a single manifold containing two disjoint copies of, with the effect of gluing to itself. For example, the connected sum of a two-sphere at two distinct points of the sphere produces the two-torus.
Read more about this topic: Connected Sum
Famous quotes containing the words local and/or operation:
“[Urging the national government] to eradicate local prejudices and mistaken rivalships to consolidate the affairs of the states into one harmonious interest.”
—James Madison (1751–1836)
“Waiting for the race to become official, he began to feel as if he had as much effect on the final outcome of the operation as a single piece of a jumbo jigsaw puzzle has to its predetermined final design. Only the addition of the missing fragments of the puzzle would reveal if the picture was as he guessed it would be.”
—Stanley Kubrick (b. 1928)