Document Type
Article
Publication Date
4-2022
Keywords
Projection complex; acylindrical hyperbolicity; weak proper discontinuity; hyperbolic quotient
Abstract
This paper is a continuation of our previous work with Margalit where we studied group actions on projection complexes. In that paper, we demonstrated sufficient conditions so that the normal closure of a family of subgroups of vertex stabilizers is a free product of certain conjugates of these subgroups. In this paper, we study both the quotient of the projection complex by this normal subgroup and the action of the quotient group on the quotient of the projection complex. We show that under certain conditions the quotient complex is δ-hyperbolic. Additionally, under certain circumstances, we show that if the original action on the projection complex was a non-elementary WPD action, then so is the action of the quotient group on the quotient of the projection complex. This implies that the quotient group is acylindrically hyperbolic.
Citation
Clay, M., & Mangahas, J. (2022). Hyperbolic Quotients of Projection Complexes. Groups, Geometry, and Dynamics, 16 (1), 225-246. https://doi.org/10.4171/GGD/646
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
