The Isomorphism Problem for Toral Relatively Hyperbolic Groups
Francois Dahmani, Daniel Groves
Abstract
We provide a solution to the isomorphism problem for torsion-free relatively hyperbolic groups with abelian parabolics. As special cases we recover solutions to the isomorphism problem for: (i) torsion-free hyperbolic groups (Sela); and (ii) fully residually free groups (Bumagin, Kharlampovich and Miasnikov). We also give a solution to the homeomorphism problem for finite volume hyperbolic n-manifolds, for n 3. In the course of the proof of the main result, we prove that a particular JSJ decomposition of a freely indecomposable torsion-free relatively hyperbolic group with abelian parabolics is algorithmically constructible.
Create a lesson
Related papers
Property R∞ for Artin and Coxeter groups whose outer automorphisms are length-preserving
Ignat Soroko
DL, DQ Spectrum and Eigenvalue-free Interval of Cayley Graphs over Finite Nilpotent Groups
Pallabi Manna, Santanu Mandal
On p-groups with one nonlinear codegree
Jiwei Zheng, Heng Lv
Classes of Subgroups of a finite group with isomorphic quotient groups
Tushar Halder, Sachin Ballal
Cohomology and multiplicative gaps for quasi-isometries of nilpotent groups
Mayukh Mukherjee, Soumyadeb Samanta, Soumyadip Thandar
On the number of conjugacy classes of finite solvable groups of order divisible by p2
Thomas Michael Keller