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 Mathematics32 (2001) suppl.2 Abstract: In previous results, Bleiler and Nakanishi produced an example ofa knot where the unknotting number was not realized in a minimal projectionof the knot. Bernhard generalied this example to an infi{}nite classof examples with Conway notation $\left(2j+1,1,2j\right)$ with j$\geq$ 2. In this paper we examine the entire class of knots givenin 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 formhave the unknotting number not realized in a minimal projection. Wealso produce an infi{}nite class of two component links with unknottingnumber 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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