Knot adjacency and satellites

dc.creatorKalfagianni, Efstratia
dc.creatorLin, Xiao-Song
dc.date2003-08-18
dc.date.accessioned2026-07-07T05:00:28Z
dc.date.available2026-07-07T05:00:28Z
dc.descriptionA knot K is called n-adjacent to the unknot, if K admits a projection containing n generalized crossings such that changing any m (no larger than n) of them yields a projection of the unknot. We show that a non-trivial satellite knot K is n-adjacent to the unknot, for some n>0, if and only if it is n-adjacent to the unknot in any companion solid torus. In particular, every model knot of K is n-adjacent to the unknot. Along the way of proving these results, we also show that 2-bridge knots of the form K_{p/q}, where p/q=[2q_1,2q_2] for some integers q_1,q_2, are precisely those knots that have genus one and are 2-adjacent to the unknot.
dc.description13 pages, 3 figures. to appear in Topology and Its Applications
dc.identifierhttps://arxiv.org/abs/math/0308168
dc.identifierhttp://arxiv.org/abs/math/0308168
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68337
dc.subjectGeometric Topology
dc.titleKnot adjacency and satellites
dc.typetext

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