- White (1969): A
singly encircled band with two half-twists is topologically equivalent to a doubly-encircled untwisted band.
- Cãlugãreanu/Fuller: The Linking number describes both forms, and comprises;
Lk = Tw + Wr
Wr or Writhe measures the extent to which coiling of the
central curve has relieved local twisting T of the
ribbon (Tw is ∫T)
-
- Positive values of Wr are termed overtwisting by supercoiling
- Negative values of Wr are termed undertwisting by supercoiling
The White, Cãlugãreanu, Fuller Theorem; J. H. White, Am. J. Math., 1969,
91, 693-728; G. Cãlugãreanu,
Czech Mathematics J., 1961, 11, 588-625;
F. Fuller, Proc. Natl. Acad. Sci.,
1971, 68, 815-819.