Outer automorphism groups of one-ended hyperbolic groups are virtually hierarchically hyperbolic under orientability conditions on JSJ decompositions, via bounded central extensions of orbifold mapping class groups, with a sharpness counterexample.
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Ergodic mapping class group invariant measures on Deroin-Tholozan character varieties are either counting measures on finite orbits or the Liouville measure from the Goldman symplectic form.
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Outer automorphism groups of hyperbolic groups, bounded extensions, and hierarchical hyperbolicity
Outer automorphism groups of one-ended hyperbolic groups are virtually hierarchically hyperbolic under orientability conditions on JSJ decompositions, via bounded central extensions of orbifold mapping class groups, with a sharpness counterexample.
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Invariant measures for Deroin-Tholozan representations
Ergodic mapping class group invariant measures on Deroin-Tholozan character varieties are either counting measures on finite orbits or the Liouville measure from the Goldman symplectic form.