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 Sn+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.