Unknotting numbers of diagrams of a given nontrivial knot are unbounded

dc.creatorTaniyama, Kouki
dc.date2008-05-20
dc.date2008-06-22
dc.date.accessioned2026-07-07T09:45:42Z
dc.date.available2026-07-07T09:45:42Z
dc.descriptionWe show that for any nontrivial knot $K$ and any natural number $n$ there is a diagram $D$ of $K$ such that the unknotting number of $D$ is greater than or equal to $n$. It is well known that twice the unknotting number of $K$ is less than or equal to the crossing number of $K$ minus one. We show that the equality holds only when $K$ is a $(2,p)$-torus knot.
dc.description13 pages, 14 figures. Theorem 1.4 and Theorem 1.5 added
dc.identifierhttps://arxiv.org/abs/0805.3174
dc.identifierhttp://arxiv.org/abs/0805.3174
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163286
dc.subjectGeometric Topology
dc.subject57M25
dc.titleUnknotting numbers of diagrams of a given nontrivial knot are unbounded
dc.typetext

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