Kathrynn Mann, Jason Fox Manning, Theodore Weisman
Add an identifier
Abstract:A hyperbolic group acts by homeomorphisms on its Gromov boundary. We use a
dynamical coding of boundary points to show that such actions are topologically
stable in the dynamical sense: any nearby action is semi-conjugate to (and an
extension of) the standard boundary action.
In theorem 1.1 the authors prove that the standard action of a hyperbolic group on its Gromov boundary is stable up to a semi conjugacy.
They show that the result is not true if hyperbolic is replaced by relatively hyperbolic and the Gromov boundary is replaced by the Bowditch boundary.
For hyperbolic groups if we replace the Gromov boundary with another boundary such as the Poisson boundary is the action stable and if so
can it be proved using the dynamical coding techniques in this paper?