Structural stability of meandering-hyperbolic group actions
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Structural stability of meandering-hyperbolic group actions

  • Author(s): Kapovich, Michael;
  • Kim, Sungwoon;
  • Lee, Jaejeong
  • et al.
Abstract

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.

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