Band sum

{{Short description|Method of connecting knots}}

In geometric topology, a band sum of two n-dimensional knots K₁ and K₂ 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 (K₁, K₂) embedded in Sⁿ⁺².
• There are points $p\_1\backslash in\; K\_1$ and $p\_2\backslash in\; K\_2$ such that $h$ is attached to $K\_1\backslash sqcup\; K\_2$ along $p\_1\backslash sqcup\; p\_2$.

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

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