论文标题
三态组的叠层层状结构通过准晶体
Equivariant hierarchically hyperbolic structures for 3-manifold groups via quasimorphisms
论文作者
论文摘要
Behrstock，Hagen和Sisto分类了三个曼佛组，承认了分层双曲线的空间结构。但是，这些结构并不总是相对于该组的均等。在本文中，我们对承认层次分层结构的3个manifold组进行了分类。我们证明的关键组成部分是，克罗克和克莱纳引入的可接受的群体始终承认层次分层的双曲线结构。对于非几何图形歧管，这与Behrstock，Hagen和Sisto的猜想相反，并且与这些组上CAT（0）立方结构的结果形成对比。也许令人惊讶的是，我们的论点涉及在Seifert碎片上构建合适的准畸形，以便在准线上构建行动。
Behrstock, Hagen, and Sisto classified 3-manifold groups admitting a hierarchically hyperbolic space structure. However, these structures were not always equivariant with respect to the group. In this paper, we classify 3-manifold groups admitting equivariant hierarchically hyperbolic structures. The key component of our proof is that the admissible groups introduced by Croke and Kleiner always admit equivariant hierarchically hyperbolic structures. For non-geometric graph manifolds, this is contrary to a conjecture of Behrstock, Hagen, and Sisto and also contrasts with results about CAT(0) cubical structures on these groups. Perhaps surprisingly, our arguments involve the construction of suitable quasimorphisms on the Seifert pieces, in order to construct actions on quasi-lines.
