Band sum

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 S^{n + 2}.
• There are points and such that h is attached to along .

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

A band sum is thus a generalization of the usual knot sum.

See also

• Manifold decomposition
• Connected sum