Quotients of the curve complex

Joseph Maher, Hidetoshi Masai, Saul Schleimer

Published 2020-10-26Version 1

We consider three kinds of quotients of the curve complex which are obtained by coning off uniformly quasi-convex 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 WPD, which implies that the actions are non-elementary and those quotients are of infinite diameter.