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Jan 23, 2017 at 7:07 comment added HJRW Relatedly, if the Gromov boundary of a hyperbolic group $G$ is a circle, then the Convergence Group Theorem of Casson--Jungreis--Gabai--Tukia asserts that $G$ is finite-by-Fuchsian.
Jan 22, 2017 at 16:33 history answered Richard Weidmann CC BY-SA 3.0