Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4287
Title: Unknotting Numbers are not Realized in Minimal Projections for a Class of Rational Knots
Authors: Garity, Dennis J.
Issue Date: 2001
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.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
32 (2001) suppl.2
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.
Type: Article
URI: http://hdl.handle.net/10077/4287
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.32 (2001) s2

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