Some examples of separable convex-cocompact subgroups
Mark Hagen, Alessandro Sisto
TL;DR
This paper provides new examples of separable convex-cocompact subgroups in mapping class groups, specifically free groups of arbitrary finite rank, expanding beyond previously known virtually cyclic cases.
Contribution
It introduces a construction that produces separable convex-cocompact subgroups of arbitrary finite rank, addressing a question posed by Reid.
Findings
Existence of separable convex-cocompact free subgroups of arbitrary rank
Construction based on Manning-Mj-Sageev method
Examples extend beyond virtually cyclic subgroups
Abstract
Reid asked whether all convex-cocompact subgroups of mapping class groups are separable. Using a construction of Manning-Mj-Sageev, we give examples of separable convex-cocompact subgroups that are free of arbitrary finite rank, while prior examples seem to all be virtually cyclic.
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Taxonomy
TopicsFinite Group Theory Research · Geometric and Algebraic Topology · Rings, Modules, and Algebras