Editing Connected sum (section)

== Local operation ==

The connected sum is a local operation on manifolds, meaning that it alters the summands only in a [[neighborhood (mathematics)|neighborhood]] of <math>V</math>. This implies, for example, that the sum can be carried out on a single manifold <math>M</math> containing two [[Disjoint sets|disjoint]] copies of <math>V</math>, with the effect of gluing <math>M</math> to itself. For example, the connected sum of a 2-sphere at two distinct points of the sphere produces the 2-torus.