9 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,…
(Non-)existence of Cannon-Thurston maps for Morse boundaries
Ruth Charney, Matthew Cordes, Antoine Goldsborough +2
We show that the Morse boundary exhibits interesting examples of both the existence and non-existence of Cannon-Thurston maps for normal subgroups, in contrast with the hyperbolic…
Hyperbolic spaces that detect all strongly-contracting directions
Stefanie Zbinden
Given a geodesic metric space , we construct a corresponding hyperbolic space, which we call the contraction space, that detects all strongly contracting directions in the follo…
Subgroups arising from connected components in the Morse boundary
Annette Karrer, Babak Miraftab, Stefanie Zbinden
We study connected components of the Morse boundary and their stabilisers. We introduce the notion of point-convergence and show that if the set of non-singleton connected componen…