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arXiv · 2605.23829

Outer automorphism groups of hyperbolic groups, bounded extensions, and hierarchical hyperbolicity

Ervin Hadziosmanovic·Giorgio Mangioni
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Abstract

We prove that the outer automorphism group of a one-ended hyperbolic group is virtually a hierarchically hyperbolic group (HHG), under mild orientability conditions on the associated JSJ decomposition. This is done by proving that a finite-index subgroup is a central extension of a product of orbifold mapping class groups, and the extension has bounded Euler class. Our theorem is sharp: we exhibit a surface amalgam whose fundamental group has full outer automorphism group which is not a HHG.

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Ervin Hadziosmanovic, Giorgio Mangioni. 2026-05-22. Outer automorphism groups of hyperbolic groups, bounded extensions, and hierarchical hyperbolicity. https://arxiv.org/abs/2605.23829

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