持久层状分枝面

摘要：

我们定义的分支复合物的下沉标记，并找到他们的条件，以确定一个分支的表面结构。这些将被用来构建结和缠结补的分支曲面。我们将推广Delman定理，证明一个长度至少为3的Montesinos结$K$有一个持续的层状分支曲面，除非它对某些正整数$q_i$等价于$K(1/2q_1,\, 1/q_2,\, 1/q_3,\, -1)$.在大多数情况下，这些分支表面是真实的，在这种情况下，$K$不允许进行环形塞弗特纤维手术。它也将表明，有许多持续的层状缠结。

英文摘要：

We define sink marks for branched complexes and find conditions for them to determine a branched surface structure. These will be used to construct branched surfaces in knot and tangle complements. We will extend Delman's theorem and prove that a Montesinos knot $K$ of length at least 3 has a persistently laminar branched surface unless it is equivalent to $K(1/2q_1,\, 1/q_2,\, 1/q_3,\, -1)$ for some positive integers $q_i$. In most cases these branched surfaces are genuine, in which case $K$ admits no atoroidal Seifert fibered surgery. It will also be shown that there are many persistently laminar tangles.

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