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…
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…
Graphs and groups with unique geodesics
Murray Elder, Giles Gardam, Adam Piggott +2
A connected graph is called \emph{geodetic} if there is a unique geodesic between each pair of vertices. In this paper we prove that if a finitely generated group admits a Cayley g…
Non-trivial units of complex group rings
Giles Gardam
The Kaplansky unit conjecture for group rings is false in characteristic zero.