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 <math>p_1\in K_1</math> and <math>p_2\in K_2</math> such that <math>h</math> is attached to <math>K_1\sqcup K_2</math> along <math>p_1\sqcup p_2</math>.

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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