solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看168次
Largest acylindrical actions and stability in hierarchically hyperbolic groups. (arXiv:1705.06219v1 [math.GR])
来源于:arXiv
We consider two manifestations of non-positive curvature: acylindrical
actions (on hyperbolic spaces) and quasigeodesic stability. We study these
properties for the class of hierarchically hyperbolic groups, which is a
general framework for simultaneously studying many important families of
groups, including mapping class groups, right-angled Coxeter groups, most
3-manifold groups, right-angled Artin groups, and many others.
A group that admits an acylindrical action on a hyperbolic space may admit
many such actions on different hyperbolic spaces. It is natural to try to
develop an understanding of all such actions and to search for a "best" one.
The set of all cobounded acylindrical actions on hyperbolic spaces admits a
natural poset structure, and in this paper we prove that all hierarchically
hyperbolic groups admit a unique action which is the largest in this poset. The
action we construct is also universal in the sense that every element which
acts loxodromically in some acylindri 查看全文>>