Band sum

In geometric topology, a band sum of two n-dimensional knots K₁ and K₂ along an -dimensional 1-handle h called a band is an n-dimensional knot K such that:

There is an -dimensional 1-handle h connected to embedded in Sⁿ⁺².
There are points and such that is attached to along.

K is the n-dimensional knot obtained by this surgery.
A band sum is thus a generalization of the usual connected sum of knots.