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Unknotting Numbers are not Realized in Minimal Projections for a Class of Rational Knots
Garity, Dennis J.
2001
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 $\left(2j+1,1,2j\right)$ with j
$\geq$ 2. In this paper we examine the entire class of knots given
in Conway notation by (2j + 1, 2k + 1, 2j) where j $\geq$ 1 and k
$\geq$ 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.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
32 (2001) suppl.2
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
Dennis J. Garity, "Unknotting Numbers are not Realized in Minimal Projections for a Class of Rational Knots", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 32 (2001) suppl.2, pp. 59–72.
Languages
en
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