标题： 旋转和随机商保持分层双曲性 显示英文标题

标题： Spinning and random quotients preserve hierarchical hyperbolicity

摘要： 在本文中，我们考虑通过将分层超双曲群对一个有限族独立随机游走的第n步进行商得到的随机商群。我们证明，分层超双曲群的随机商群几乎必然地仍然是分层超双曲群。同样的技术还得出，非初等双曲群（相对于一个有限的外围子群族）的随机商群几乎必然地是双曲的（相对于同构的外围子群）。我们的主要工具来自旋转族和投影复形理论，我们进一步发展了这些理论。 显示英文摘要

摘要： In this paper we consider random quotients of hierarchically hyperbolic groups, obtained by taking the quotient of the group by the n-th steps of a finite family of independent random walks. We show that a random quotient of a hierarchically hyperbolic group is again hierarchically hyperbolic asymptotically almost surely. The same techniques also yield that a random quotient of a non-elementary hyperbolic group (relative to a finite collection of peripheral subgroups) is asymptotically almost surely hyperbolic (relative to isomorphic peripheral subgroups). Our main tools come from the theory of spinning families and projection complexes, which we further develop.