## ::Connected sum

### ::concepts

Knots::along Oriented::setminus Manifold::''l'' Sum'''::''k'' Disjoint::together Choice::which

In mathematics, specifically in topology, the operation of **connected sum** is a geometric modification on manifolds. Its effect is to join two given manifolds together near a chosen point on each. This construction plays a key role in the 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 on knots, called the **knot sum** or **composition** of knots.

**Connected sum sections**

Intro Connected sum at a point Connected sum along a submanifold Connected sum along a codimension-two submanifold Local operation Connected sum of knots See also Further reading

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