Operations on structures | Geometric topology | Differential topology | Knot theory

Connected sum

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. (Wikipedia).

Connected sum
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Knot genus | Normal bundle | Homotopy | Homeomorphism | Topology | Ambient space | Satellite knot | Knot (mathematics) | Cohomology | Disjoint sets | Manifold decomposition | Euler class | Torus | Ball (mathematics) | Mathematics | Prime knot | Real projective plane | Diffeomorphism | Sphere | Embedding | Identity (mathematics) | Circle group | Category (mathematics) | Band sum | Manifold | Exotic sphere | Symplectic sum | Symplectic manifold | Disc theorem | Adjunction space | Surface (topology) | Monoid