Band Sum

In geometric topology, a band sum of two ''n''-dimensional knots ''K''₁ and ''K''₂ along an (''n'' + 1)-dimensional 1-handle ''h'' called a ''band'' is an ''n''-dimensional knot ''K'' such that:

* There is an (''n'' + 1)-dimensional 1-handle ''h'' connected to (''K''₁, ''K''₂) embedded in ''S''^''n''+2.
* There are points $p_1\in K_1$ and $p_2\in K_2$ such that $h$ is attached to $K_1\sqcup K_2$ along $p_1\sqcup p_2$.

''K'' is the ''n''-dimensional knot obtained by this surgery.

A band sum is thus a generalization of the usual connected sum of knots.

See also

*Manifold decomposition

References

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Topology
Differential topology
Knot theory
Operations on structures

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