Acylindrical hyperbolicity of outer automorphism groups of right-angled Artin groups
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913083873558528 |
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| author | Baik, Hyungryul Kim, Junseok |
| author_facet | Baik, Hyungryul Kim, Junseok |
| contents | We study the acylindrical hyperbolicity of the outer automorphism group of a right-angled Artin group $A_Γ$. When the defining graph $Γ$ has no SIL-pair (separating intersection of links), we obtain a necessary and sufficient condition for $\mathrm{Out}(A_Γ)$ to be acylindrically hyperbolic. As a corollary, if $Γ$ is a random connected graph satisfying a certain probabilistic condition, then $\mathrm{Out}(A_Γ)$ is not acylindrically hyperbolic with high probability. When $Γ$ has a maximal SIL-pair system, we derive a classification theorem for partial conjugations. Such a classification theorem allows us to show that the acylindrical hyperbolicity of $\mathrm{Out}(A_Γ)$ is closely related to the existence of a specific type of partial conjugations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_19702 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Acylindrical hyperbolicity of outer automorphism groups of right-angled Artin groups Baik, Hyungryul Kim, Junseok Group Theory We study the acylindrical hyperbolicity of the outer automorphism group of a right-angled Artin group $A_Γ$. When the defining graph $Γ$ has no SIL-pair (separating intersection of links), we obtain a necessary and sufficient condition for $\mathrm{Out}(A_Γ)$ to be acylindrically hyperbolic. As a corollary, if $Γ$ is a random connected graph satisfying a certain probabilistic condition, then $\mathrm{Out}(A_Γ)$ is not acylindrically hyperbolic with high probability. When $Γ$ has a maximal SIL-pair system, we derive a classification theorem for partial conjugations. Such a classification theorem allows us to show that the acylindrical hyperbolicity of $\mathrm{Out}(A_Γ)$ is closely related to the existence of a specific type of partial conjugations. |
| title | Acylindrical hyperbolicity of outer automorphism groups of right-angled Artin groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2405.19702 |