Average Distortion of Commensurators of Hyperbolic Groups
We prove that commensurators of a geometrically rigid residually finite hyperbolic group have bounded average distortion.
math.GR↗
arXiv subjects
Suraj Krishna M S
Publications and source records attributed to Suraj Krishna M S.
Random Quotients of Free Products
We introduce a density model for random quotients of a free product of finitely generated groups. We prove that a random quotient in this model has the following properties with overwhelming probability: if the density is below $1/2$, the free factors embed into the random quotient and the random quotient is hyperbolic relative to the free factors. Further, there is a phase transition at $1/2$, with the random quotient being a finite group above this density. If the density is below $1/6$, the random quotient is cubulated relative to the free factors. Moreover, if the free factors are cubulated, then so is the random quotient.
math.GR↗
Cubulating a free-product-by-cyclic group
Let $G = H_1 * ... * H_k * F_r$ be a torsion-free group and $ϕ$ an automorphism of $G$ that preserves this free factor system. We show that when $ϕ$ is fully irreducible and atoroidal relative to this free factor system, the mapping torus $Γ= G \rtimes_ϕ \mathbb{Z}$ acts relatively geometrically on a hyperbolic CAT(0) cube complex. This is a generalisation of a result of Hagen and Wise for hyperbolic free-by-cyclic groups.
math.GR↗
Hyperbolic hyperbolic-by-cyclic groups are cubulable
We show that the mapping torus of a hyperbolic group by a hyperbolic automorphism is cubulable. Along the way, we (i) give an alternate proof of Hagen and Wise's theorem that hyperbolic free-by-cyclic groups are cubulable, and (ii) extend to the case with torsion Brinkmann's thesis that a torsion-free hyperbolic-by-cyclic group is hyperbolic if and only if it does not contain $\mathbb{Z}^2$-subgroups.
math.GR↗
Relatively hyperbolic groups with strongly shortcut parabolics are strongly shortcut
We show that a group that is hyperbolic relative to strongly shortcut groups is itself strongly shortcut, thus obtaining new examples of strongly shortcut groups. The proof relies on a result of independent interest: we show that every relatively hyperbolic group acts properly and cocompactly on a graph in which the parabolic subgroups act properly and cocompactly on convex subgraphs.
math.GR↗
Vertex links and the Grushko decomposition
We develop an algorithm of polynomial time complexity to construct the Grushko decomposition of fundamental groups of graphs of free groups with cyclic edge groups. Our methods rely on analysing vertex links of certain CAT(0) square complexes naturally associated with a special class of the above groups. Our main result transforms a one-ended CAT(0) square complex of the above type to one whose vertex links satisfy a strong connectivity condition, as first studied by Brady and Meier.
math.GR↗
Relative hyperbolicity of hyperbolic-by-cyclic groups
Let $G$ be a torsion-free hyperbolic group and $α$ an automorphism of $G$. We show that there exists a canonical collection of subgroups that are polynomially growing under $α$, and that the mapping torus of $G$ by $α$ is hyperbolic relative to the suspensions of the maximal polynomially growing subgroups under $α$.
math.GR↗
Immersed cycles and the JSJ decomposition
We present an algorithm to construct the JSJ decomposition of one-ended hyperbolic groups which are fundamental groups of graphs of free groups with cyclic edge groups. Our algorithm runs in double exponential time, and is the first algorithm on JSJ decompositions to have an explicit time bound. Our methods are combinatorial/geometric and rely on analysing properties of immersed cycles in certain CAT(0) square complexes.
math.GR↗