Completely tubing compressible tangles and standard graphs in genus one 3-manifolds

dc.creatorWu, Ying-Qing
dc.date2000-11-01
dc.date.accessioned2026-07-07T04:38:24Z
dc.date.available2026-07-07T04:38:24Z
dc.descriptionWe prove a conjecture of Menasco and Zhang that if a tangle is completely tubing compressible then it consists of at most two families of parallel strands. This is related to problems of graphs in 3-manifold. A 1-vertex graph $Γ$ in a 3-manifold $M$ with a genus 1 Heegaard splitting is standard if it consists of one or two parallel sets of core curves lying in the Heegaard splitting solid tori of $M$ in the standard way. The above conjecture then follows from the theorem which says that a 1-vertex graph in $M$ is standard if and only if the exteriors of all its nontrivial subgraphs are handlebodies.
dc.description7 pages, 0 figures
dc.identifierhttps://arxiv.org/abs/math/0011007
dc.identifierhttp://arxiv.org/abs/math/0011007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60267
dc.subjectGeometric Topology
dc.subject57N10
dc.titleCompletely tubing compressible tangles and standard graphs in genus one 3-manifolds
dc.typetext

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