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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 p_{1}\in K_{1} and p_{2}\in K_{2} such that h is attached to K_{1}\coprod K_{2} along p_{1}\coprod p_{2}.

K is the n-dimensional knot obtained by this surgery.

A band sum is thus a generalization of the usual knot sum.

See also

Science Fair Project Encyclopedia Contents Page
10-26-2009 08:16:03
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