Band sum

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Short description: Method of connecting knots

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 (K1K2) embedded in Sn+2.
  • There are points p1K1 and p2K2 such that h is attached to K1K2 along p1p2.

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

References