亏格为1的3-流形中的完全管状可压缩缠结与标准图
Completely tubing compressible tangles and standard graphs in genus one 3-manifolds
摘要：
我们证明了一个猜想Menasco和张，如果一个纠结是完全管可压缩的，那么它由最多两个家庭的平行股。这与三维流形中的图的问题有关。一个亏格为1的3-流形$M$中的1-顶点图$Γ$是标准的，如果它由一组或两组平行的核心曲线以标准方式位于$M$的Heegaard分裂实环面中.上面的猜想则来自于一个定理，该定理说$M$中的一个1-顶点图是标准的当且仅当它的所有非平凡子图的外部都是标准体。
英文摘要：
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.
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