Editing Connected sum (section)

{{Short description|Way to join two given mathematical manifolds together}}
[[Image:Connected sum.svg|right|thumb|Illustration of connected sum.]]

In [[mathematics]], specifically in [[topology]], the operation of '''connected sum''' is a geometric modification on [[manifold]]s. Its effect is to join two given manifolds together near a chosen point on each. This construction plays a key role in the [[Surface (topology)#Classification of closed surfaces|classification of closed surfaces]].

More generally, one can also join manifolds together along identical submanifolds; this generalization is often called the '''fiber sum'''. 

There is also a closely related notion of a [[#Connected sum of knots|connected sum]] on [[knot (mathematics)|knot]]s, called the '''knot sum''' or '''composition''' of knots.