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::Connected sum

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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.

Illustration of connected sum.

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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