Structural stability of meandering-hyperbolic group actions
Abstract
In his 1985 paper Sullivan sketched a proof of his structural stability theorem for differentiable group actions satisfying certain expansion-hyperbolicity axioms. In this paper we relax Sullivan's axioms and introduce a notion of "meandering hyperbolicity" for group actions on geodesic metric spaces. This generalization is substantial enough to encompass actions of certain non-hyperbolic groups, such as actions of "uniform lattices" in semisimple Lie groups on flag manifolds. At the same time, our notion is sufficiently robust and we prove that meandering-hyperbolic actions are still structurally stable. We also prove some basic results on meandering-hyperbolic actions and give other examples of such actions.
Cite
@article{arxiv.1904.06921,
title = {Structural stability of meandering-hyperbolic group actions},
author = {Michael Kapovich and Sungwoon Kim and Jaejeong Lee},
journal= {arXiv preprint arXiv:1904.06921},
year = {2022}
}
Comments
59 pages, 5 figures; [v4] Incorporated referee's suggestions, revised the introduction and reorganized subsections. To appear in Journal of the Institute of Mathematics of Jussieu