5 papers · 1 filter
Weak rank rigidity for groups with a navigable path system
Cornelia Drutu, Davide Spriano, Stefanie Zbinden
We show that groups with a mild form of non-positive curvature (a navigable path system) satisfy the weak rank rigidity conjecture: they either have linear divergence or a Morse el…
Almost planar finitely presented groups
John M. Mackay, Joseph P. MacManus, Davide Spriano
We show that finitely presented groups which admit -planar Cayley graphs contain finite-index subgroups with planar Cayley graphs. More generally, we answer a question of Georga…
Weak Morse properties in spaces with bounded combings
Cornelia Drutu, Davide Spriano, Stefanie Zbinden
We relate two notions of non-positive curvature: bounded combings and the Morse local-to-global (MLTG) property (in its weak and strong version). The latter is a property of a spac…
Sigma-compactness of Morse boundaries in Morse local-to-global groups and applications to stationary measures
Vivian He, Davide Spriano, Stefanie Zbinden
We show that the Morse boundary of a Morse local-to-global group is -compact. Moreover, we show that the converse holds for small cancellation groups. As an application, we show…
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…