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.
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