在大距离上允许环形和环面填充的双曲三维流形的边界结构
Boundary structures of hyperbolic 3-manifolds admitting annular and toroidal fillings at large distance
摘要：
对于具有环面边界分量的双曲三维流形$M$，除了1000个Dehn填充之外，所有的Dehn填充都产生双曲三维流形。在本文中，我们将集中在情况下，$M$有两个特殊的德恩填充：环形填充和环形填充。对于这种情形，Gordon给出了两个坡之间距离的上界δ.此外，距离4仅由两个特定的歧管实现，而距离5由单个歧管实现。这些流形都有两个环面的并集作为它们的边界。此外，有一个流形的三个环面作为其边界，实现了距离3。我们表明，如果距离是三个，那么边界的歧管由最多三个环面。
英文摘要：
For a hyperbolic 3-manifold $M$ with a torus boundary component,all but finitely many Dehn fillings yield hyperbolic 3-manifolds. In this paper, we will focus on the situation where $M$ has two exceptional Dehn fillings: an annular filling and a toroidal filling. For such situation, Gordon gave an upper bound 5 for the distance between such slopes. Furthermore, the distance 4 is realized only by two specific manifolds, and 5 is realized by a single manifold. These manifolds all have a union of two tori as their boundaries. Also, there is a manifold with three tori as its boundary which realizes the distance 3. We show that if the distance is three then the boundary of the manifold consists of at most three tori.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
