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Band sum

From Wikipedia, the free encyclopedia

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 and such that is attached to along .

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

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References

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  • Cromwell, Peter R. (2004), Knots and Links, Cambridge University Press, p. 90, ISBN 9780521548311.
  • Kawauchi, Akio (1996), Survey on Knot Theory, Springer, p. 31, ISBN 9783764351243.