论文标题
双曲线群的稳定性作用在其边界上
Stability of hyperbolic groups acting on their boundaries
论文作者
论文摘要
双曲线群通过同构在其Gromov边界上起作用。我们使用边界点的动态编码表明，这种动作在动态意义上是拓扑稳定的：附近的任何动作都是半偶联到（和扩展）标准边界动作。 在特殊情况下，该结果以前已知边界是拓扑领域。我们的证明是独立的，在这种情况下提供了有关半偶像的其他信息。当边界是一个圆圈时，我们的技术还提供了全球稳定性的新证明。
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. This result was previously known in the special case that the boundary is a topological sphere. Our proof here is independent and gives additional information about the semiconjugacy in that case. Our techniques also give a new proof of global stability when the boundary is a circle.
