7 papers
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…
Connections between the topology of the Morse boundary, the Morse local-to-global property and acylindrical hyperbolicity
Carolyn Abbott, Stefanie Zbinden
We relate the topology of the Morse boundary of a group to geometric and algorithmic properties of the group. In particular, we show that a group has -compact Morse boundary if…
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…
A non-loxodromic Morse element in a Morse local-to-global group
Carolyn Abbott, Stefanie Zbinden
We use small-cancellation techniques to construct a Morse local-to-global group G with an infinite-order Morse element that is not loxodromic in any action of G on a hyperbolic spa…
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…
Nearly-linear solution to the word problem for 3-manifold groups
Alessandro Sisto, Stefanie Zbinden
We show that the word problem for any 3-manifold group is solvable in time . Our main contribution is the proof that the word problem for admissible graphs of groups,…