Band sum explained

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.

See also

• Manifold decomposition

References

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