Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Abstract
In previous results, Bleiler and Nakanishi produced an example of
a knot where the unknotting number was not realized in a minimal projection
of the knot. Bernhard generalied this example to an infi{}nite class
of examples with Conway notation (2j+1,1,2j) with j
≥ 2. In this paper we examine the entire class of knots given
in Conway notation by (2j + 1, 2k + 1, 2j) where j ≥ 1 and k
≥ 0 and we determine that a large class of knots of this form
have the unknotting number not realized in a minimal projection. We
also produce an infi{}nite class of two component links with unknotting
number gap arbitrarily large