Trisha Shetty (Editor)

Band sum

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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 ∈ K 1 and p 2 ∈ K 2 such that h is attached to K 1 ⊔ K 2 along p 1 ⊔ 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.

    References

    Band sum Wikipedia
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