1.9 Unlinking numbers
The question of unknotting and unlinking numbers, or Gordian numbers is one of the most difficult in knot theory (Wendt, 1937; Nakanishi, 1981; Kawauchi, 1996; Kohn, 1991, 1993). In order to calculate unknotting and unlinking numbers, we need some link surgery. In every crossing of a KL it is possible to make a crossing change: to transform an overcrossing to undercrossing or vice versa.
The unlinking number u(L) of a link L is the minimal number of crossing changes required to obtain an unlink from the link L; the minimum is taken over all projections of L.
There are two different approaches for obtaining the unlinking number of L: