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.
Orbit Growth Of Contact Structures After Surgery
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Investigation of the effects of a contact surgery construction and of invariance of contact homology reveals a rich new field of inquiry at the intersection of dynamical systems and contact geometry. We produce contact 3-flows not topologically orbit-equivalent to any algebraic flow, including examples on many hyperbolic 3-manifolds, and we show how the surgery produces dynamical complexity for any Reeb flow compatible with the resulting contact structure. This includes exponential complexity when neither the surg-ered flow nor the surgered manifold are hyperbolic. We also demonstrate the use in dynamics of contact homology, a powerful tool in contact geometry.
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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.