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Structural stability of meandering-hyperbolic group actions
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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.
Forward citations
Cited by 2 Pith papers
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$C^0$ stability of boundary actions and inequivalent Anosov flows
Boundary actions of negatively curved manifold groups are C0-topologically stable, and the technique yields hyperbolic 3-manifolds with arbitrarily many topologically inequivalent Anosov flows.
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Cocompact lattice actions on flag boundaries of Euclidean buildings are topologically stable: every sufficiently small perturbation is semi-conjugate to the original action.
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