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
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