Completely tubing compressible tangles and standard graphs in genus one 3-manifolds
| dc.creator | Wu, Ying-Qing | |
| dc.date | 2000-11-01 | |
| dc.date.accessioned | 2026-07-07T04:38:24Z | |
| dc.date.available | 2026-07-07T04:38:24Z | |
| dc.description | We 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.description | 7 pages, 0 figures | |
| dc.identifier | https://arxiv.org/abs/math/0011007 | |
| dc.identifier | http://arxiv.org/abs/math/0011007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60267 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57N10 | |
| dc.title | Completely tubing compressible tangles and standard graphs in genus one 3-manifolds | |
| dc.type | text |