Almost alternating diagrams and fibered links in S^3

dc.creatorGoda, Hiroshi
dc.creatorHirasawa, Mikami
dc.creatorYamamoto, Ryosuke
dc.date1999-04-09
dc.date.accessioned2026-07-07T05:28:39Z
dc.date.available2026-07-07T05:28:39Z
dc.descriptionLet $L$ be an oriented link with an alternating diagram $D$. It is known that $L$ is a fibered link if and only if the surface $R$ obtained by applying Seifert's algorithm to $D$ is a Hopf plumbing. Here, we call $R$ a Hopf plumbing if $R$ is obtained by successively plumbing finite number of Hopf bands to a disk. In this paper, we discuss its extension so that we show the following theorem. Let $R$ be a Seifert surface obtained by applying Seifert's algorithm to an almost alternating diagrams. Then $R$ is a fiber surface if and only if $R$ is a Hopf plumbing. We also show that the above theorem can not be extended to 2-almost alternating diagrams, that is, we give examples of 2-almost alternating diagrams for knots whose Seifert surface obtained by Seifert's algorithm are fiber surfaces that are not Hopf plumbing. This is shown by using a criterion of Melvin-Morton.
dc.description18 pages, 30 figures
dc.identifierhttps://arxiv.org/abs/math/9904043
dc.identifierhttp://arxiv.org/abs/math/9904043
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78339
dc.subjectGeometric Topology
dc.subject57M25
dc.titleAlmost alternating diagrams and fibered links in S^3
dc.typetext

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