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 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.
Famous quotes containing the words band and/or sum:
“Firm, united, let us be,
Rallying round our Liberty;
As a band of brothers joined,
Peace and safety we shall find.”
—Joseph Hopkinson (1770–1842)
“I would sum up my fear about the future in one word: boring. And that’s my one fear: that everything has happened; nothing exciting or new or interesting is ever going to happen again ... the future is just going to be a vast, conforming suburb of the soul.”
—J.G. (James Graham)