标题： 最小复杂度的具有测地边界的手柄状双曲3-流形 显示英文标题

标题： Minimal complexity cusped hyperbolic 3-manifolds with geodesic boundary

摘要： 在2000年代初，Frigerio、Martelli和Petronio研究了具有双曲结构的最小组合复杂度的$3$流形。 作为这项工作的一部分，他们定义并研究了$M_{g,k}$类最小复杂度流形，这些流形具有$k$个环面尖点，并且连通的全测地边界是一个亏格为$g$的曲面。 在本文中，我们提供了$M_{k,k}$和$M_{k+1,k}$中流形的完整分类，这些情况是当亏格$g$尽可能小时的情况。 除了对$M_{k,k}$和$M_{k+1,k}$中的流形进行分类外，我们还描述了它们的等距群以及通过小斜率的德恩填充在这两组之间的关系。最后，我们给出了$M_{k,k}$中流形的重要共模不变量的描述。 显示英文摘要

摘要： In the early 2000s, Frigerio, Martelli, and Petronio studied $3$-manifolds of smallest combinatorial complexity that admit hyperbolic structures. As part of this work they defined and studied the class $M_{g,k}$ of smallest complexity manifolds having $k$ torus cusps and connected totally geodesic boundary a surface of genus $g$. In this paper, we provide a complete classification of the manifolds in $M_{k,k}$ and $M_{k+1,k}$, which are the cases when the genus $g$ is as small as possible. In addition to classifying manifolds in $M_{k,k}$, $M_{k+1,k}$, we describe their isometry groups as well as a relationship between these two sets via Dehn filling on small slopes. Finally, we give a description of important commensurability invariants of the manifolds in $M_{k,k}$.