论文标题
层次双曲线组中的无界域
Unbounded domains in hierarchically hyperbolic groups
论文作者
论文摘要
我们研究了分层双曲线组中的无界域，并在可能的分层结构上获得约束。使用这些见解，我们表征了实际上Abelian HHG的结构，并表明HHG类别在有限的扩展下未关闭。这为在准膜法下是否不变的问题提供了一个有力的答案。在此过程中，我们表明无限的扭转组不是HHG。 通过排除病理行为，我们能够为HHGS提供更简单的直接证明和综合子组定理。这涉及扩展我们的技术，以便它们适用于HHG的所有子组。
We investigate unbounded domains in hierarchically hyperbolic groups and obtain constraints on the possible hierarchical structures. Using these insights, we characterise the structures of virtually abelian HHGs and show that the class of HHGs is not closed under finite extensions. This provides a strong answer to the question of whether being an HHG is invariant under quasiisometries. Along the way, we show that infinite torsion groups are not HHGs. By ruling out pathological behaviours, we are able to give simpler, direct proofs of the rank-rigidity and omnibus subgroup theorems for HHGs. This involves extending our techniques so that they apply to all subgroups of HHGs.
