منابع مشابه
A Non-ribbon Plumbing of Fibered Ribbon Knots
A closer look at an example introduced by Livingston & Melvin and later studied by Miyazaki shows that a plumbing of two fibered ribbon knots (along their fiber surfaces) may be algebraically slice yet not ribbon. Trivially, the connected sum (i.e., 2-gonal Murasugi sum) of ribbon knots is ribbon. Non-trivially [6, 1], any Murasugi sum of fibered knots (along their fiber surfaces) is fibered. I...
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The purpose of this document is to clarify the inductive step described in the proof of Theorem 3.2 in [2]. In the second last sentence of the proof, it says, ‘it follows from the inductive proof that Rn is of index two.’ The question of how this assertion is verified was first raised by Dror Bar Natan and his student Ofer Ron [1]. To avoid any confusions that may arise in the future, the autho...
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We show that a group presented by a labelled oriented tree presentation in which the tree has diameter at most three is an HNN extension of a finitely presented group. From results of Silver, it then follows that the corresponding higher dimensional ribbon knots admit minimal Seifert manifolds. AMS Classification 57Q45; 20E06, 20F05, 57M05
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In this paper we consider minors of ribbon graphs (or, equivalently, cellularly embedded graphs). The theory of minors of ribbon graphs differs from that of graphs in that contracting loops is necessary and doing this can create additional vertices and components. Thus the ribbon graph minor relation is incompatible with the graph minor relation. We discuss excluded minor characterisations of m...
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We determine the (smooth) concordance order of the 3-stranded pretzel knots P (p, q, r) with p, q, r odd. We show that each one of finite order is, in fact, ribbon, thereby proving the slice-ribbon conjecture for this family of knots. As corollaries we give new proofs of results first obtained by Fintushel-Stern and Casson-Gordon.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1964
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1964-0171274-8