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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 [math]\displaystyle{ p_1\in K_1 }[/math] and [math]\displaystyle{ p_2\in K_2 }[/math] such that [math]\displaystyle{ h }[/math] is attached to [math]\displaystyle{ K_1\sqcup K_2 }[/math] along [math]\displaystyle{ 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

References