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.

• .

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

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