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- W2898097531 abstract "Given a (freely irreducible) product graph of groups $Gamma mathcal{G}$, we introduce and study its emph{product graph} $P(Gamma, mathcal{G})$, defined as the graph whose vertices are the maximal product subgroups of $Gamma mathcal{G}$ and whose edges link two subgroups when they intersect non-trivially. One shows that: $(i)$ $P(Gamma, mathcal{G})$ is a Gromov-hyperbolic graph which is unbounded whenever $Gamma mathcal{G}$ is not a direct sum, $(ii)$ the action $Gamma mathcal{G} curvearrowright P(Gamma, mathcal{G})$ satisfies a condition of acylindricity and induces a natural Nielsen-Thurston classification of the elements of $Gamma mathcal{G}$, $(iii)$ and this action naturally extends to an action of the automorphism group $mathrm{Aut}(Gamma mathcal{G})$. By looking for WPD isometries in the automorphism group, we prove that, if $Gamma$ is a finite, connected and square-free simplicial graph which does not decompose as a join and contains at least two vertices, then the automorphism group $mathrm{Aut}(A_Gamma)$ of the right-angled Artin group $A_Gamma$ turns out to be acylindrically hyperbolic. Applications to the geometry of cyclic extensions of right-angled Artin groups are also included." @default.
- W2898097531 created "2018-11-02" @default.
- W2898097531 creator A5016264393 @default.
- W2898097531 date "2018-07-02" @default.
- W2898097531 modified "2023-09-27" @default.
- W2898097531 title "Negative curvature of automorphism groups of graph products with applications to right-angled Artin groups" @default.
- W2898097531 hasPublicationYear "2018" @default.
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