Quotients of the curve complex

Authors

Joseph Maher, CUNY College of Staten IslandFollow
Hidetoshi Masai, Tokyo Institute of Technology
Saul Schleimer, University of Warwick

Document Type

Article

Publication Date

2024

Abstract

We consider three kinds of quotients of the curve complex, which are obtained by coning off uniformly quasiconvex subspaces: symmetric curve sets, non-maximal train track sets, and compression body disc sets. We show that the actions of the mapping class group on those quotients are strongly weakly properly discontinuously (WPD), which implies that the actions are non-elementary and those quotients are of infinite diameter.

Comments

This article was originally published in Groups, Geometry, and Dynamics, available at https://doi.org/10.4171/ggd/768

This work is published under a Creative Commons Attribution 4.0 International License.