Outer automorphism groups of hyperbolic groups, bounded extensions, and hierarchical hyperbolicity
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918518718464000 |
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| author | Hadziosmanovic, Ervin Mangioni, Giorgio |
| author_facet | Hadziosmanovic, Ervin Mangioni, Giorgio |
| contents | 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. To prove this, the main technical tool is the fact that a top-dimensional Abelian subgroup of a HHG is a standard flat. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23829 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Outer automorphism groups of hyperbolic groups, bounded extensions, and hierarchical hyperbolicity Hadziosmanovic, Ervin Mangioni, Giorgio Group Theory Geometric Topology 20F65 (Primary), 20E08, 57K20, 20J06 (Secondary) 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. To prove this, the main technical tool is the fact that a top-dimensional Abelian subgroup of a HHG is a standard flat. |
| title | Outer automorphism groups of hyperbolic groups, bounded extensions, and hierarchical hyperbolicity |
| topic | Group Theory Geometric Topology 20F65 (Primary), 20E08, 57K20, 20J06 (Secondary) |
| url | https://arxiv.org/abs/2605.23829 |