Characterizations of Stability via Morse Limit Sets

Authors

Jacob D. Garcia, Smith CollegeFollow

Document Type

Article

Publication Date

2025

Abstract

Subgroup stability is a strong notion of quasiconvexity that generalizes convex cocompactness in a variety of settings. In this paper, we characterize stability of a subgroup by properties of its limit set on the Morse boundary. Given H < G, both finitely generated, H is stable exactly when all the limit points of H are conical, or equivalently when all the limit points of H are horospherical, as long as the limit set of H is a compact subset of the Morse boundary for G We also demonstrate an application of these results in the settings of the mapping class group for a finite type surface, Mod(S).

Version

Author's Accepted Manuscript

Comments

Accepted for Publication in Algebraic & Geometric Topology, expected publication date in early 2026.

Recommended Citation

Garcia, Jacob D., "Characterizations of Stability via Morse Limit Sets" (2025). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/199