arXiv subjects
Publications and source records attributed to Alexander Taam.
Let $Γ$ be a word hyperbolic group with a cyclic JSJ decomposition that has only rigid vertex groups, which are all fundamental groups of closed surface groups. We show that any group $H$ quasi-isometric to $Γ$ is abstractly commensurable with $Γ$.
We show that, given a finitely generated group $G$ as the coordinate group of a finite system of equations over a torsion-free hyperbolic group $Γ$, there is an algorithm which constructs a cover of a canonical solution diagram. The diagram encodes all homomorphisms from $G$ to $Γ$ as compositions of factorizations through $Γ$-NTQ groups and canonical automorphisms of the corresponding NTQ-subgroups. We also give another characterization of $Γ$-limit groups as iterated generalized doubles over $Γ$.