JournalsggdVol. 18, No. 2pp. 379–405

Quotients of the curve complex

  • Joseph Maher

    CUNY College of Staten Island and CUNY Graduate Center, Staten Island, USA

  • Hidetoshi Masai

    Tokyo Institute of Technology, Tokyo, Japan

  • Saul Schleimer

    University of Warwick, Coventry, UK
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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.

Cite this article

Joseph Maher, Hidetoshi Masai, Saul Schleimer, Quotients of the curve complex. Groups Geom. Dyn. 18 (2024), no. 2, pp. 379–405

DOI 10.4171/GGD/768