4 papers
JSJ decompositions and polytopes for two-generator one-relator groups
Giles Gardam, Dawid Kielak, Alan D. Logan
We provide a direct connection between the Z_{max} (or essential) JSJ decomposition and the Friedl--Tillmann polytope of a hyperbolic two-generator one-relator group with abelianis…
Fixed subgroups of generalised Baumslag-Solitar groups
Oli Jones, Alan Logan
We investigate fixed subgroups of automorphisms of generalised Baumslag-Solitar (GBS) groups. Our main results are for automorphisms leaving a Bass-Serre tree invariant, under the…
The Conjugacy Problem for ascending HNN-extensions of free groups
Alan D. Logan
We give an algorithm to solve the Conjugacy Problem for ascending HNN-extensions of free groups. To do this, we give algorithms to solve certain problems on dynamics of free group…
Algebraically hyperbolic groups
Giles Gardam, Dawid Kielak, Alan D. Logan
We initiate the study of torsion-free algebraically hyperbolic groups; these groups generalise torsion-free hyperbolic groups and are intricately related to groups with no Baumslag…