Quotients of the curve complex
Joseph Maher, Hidetoshi Masai, Saul Schleimer
TL;DR
This paper studies three types of quotients of the curve complex formed by coning off specific quasi-convex subspaces, demonstrating that the mapping class group acts strongly WPD on them, leading to non-elementary actions and infinite diameter quotients.
Contribution
It introduces and analyzes three new quotients of the curve complex, establishing their properties under the mapping class group action and proving they have infinite diameter.
Findings
Actions are strongly WPD on all quotients
Actions are non-elementary
Quotients have infinite diameter
Abstract
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Point processes and geometric inequalities · Geometry and complex manifolds