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 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. See also Manifold decomposition References . . Topology Differential topology Knot theory Operations on structures