Structural stability of meandering-hyperbolic group actions
- Author(s): Kapovich, Michael;
- Kim, Sungwoon;
- Lee, Jaejeong
- et al.
In his 1985 paper Sullivan sketched a proof of his structural stability theorem for 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 general 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.