Tim Susse
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View article: Outer automorphism groups of graph products: subgroups and quotients
Outer automorphism groups of graph products: subgroups and quotients Open
We show that the outer automorphism groups of graph products of finitely\ngenerated abelian groups satisfy the Tits alternative, are residually finite,\ntheir so-called Torelli subgroups are finitely generated, and they satisfy a\ndichotom…
View article: Square percolation and the threshold for quadratic divergence in random right‐angled Coxeter groups
Square percolation and the threshold for quadratic divergence in random right‐angled Coxeter groups Open
Given a graph , its auxiliary square‐graph is the graph whose vertices are the non‐edges of and whose edges are the pairs of non‐edges which induce a square (i.e., a 4‐cycle) in . We determine the threshold edge‐probability at which the Er…
View article: Morse subgroups and boundaries of random right-angled Coxeter groups
Morse subgroups and boundaries of random right-angled Coxeter groups Open
We study Morse subgroups and Morse boundaries of random right-angled Coxeter groups in the Erdős--Rényi model. We show that at densities below $\left(\sqrt{\frac{1}{2}}-ε\right)\sqrt{\frac{\log{n}}{n}}$ random right-angled Coxeter groups a…
View article: Automaticity for graphs of groups
Automaticity for graphs of groups Open
In this article we construct asynchronous and sometimes synchronous automatic structures for amalgamated products and HNN extensions of groups that are strongly asynchronously (or synchronously) coset automatic with respect to the associat…
View article: Outer automorphism groups of right-angled Coxeter groups are either large or virtually abelian
Outer automorphism groups of right-angled Coxeter groups are either large or virtually abelian Open
We generalize the notion of a separating intersection of links (SIL) to give necessary and sufficient criteria on the defining graph of a right-angled Coxeter group so that its outer automorphism group is large: that is, it contains a fi…
View article: Outer automorphism groups of right-angled Coxeter groups are either\n large or virtually abelian
Outer automorphism groups of right-angled Coxeter groups are either\n large or virtually abelian Open
We generalise the notion of a separating intersection of links (SIL) to give\nnecessary and sufficient criteria on the defining graph $\\Gamma$ of a\nright-angled Coxeter group $W_\\Gamma$ so that its outer automorphism group is\nlarge: th…
View article: Global Structural Properties of Random Graphs
Global Structural Properties of Random Graphs Open
We study two global structural properties of a graph $\\Gamma$, denoted AS and\nCFS, which arise in a natural way from geometric group theory. We study these\nproperties in the Erd\\"os--R\\'enyi random graph model G(n,p), proving a sharp\…
View article: Hierarchical hyperbolicity of all cubical groups
Hierarchical hyperbolicity of all cubical groups Open
Let X be a proper CAT(0) cube complex admitting a proper cocompact action by a group G, then X has a factor system in the sense of [BHS14]. By results of Behrstock--Hagen--Sisto it follows that G is a hierarchically hyperbolic group; this …