4 papers · 1 filter
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…
Homotopy types of complexes of hyperplanes in quasi-median graphs and applications to right-angled Artin groups
Carolyn Abbott, Anthony Genevois, Eduardo Martinez-Pedroza
In this article, we prove that, given two finite connected graphs and , if the two right-angled Artin groups and are quasi-isometric, then the infinite…
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…
The quasi-isometry invariance of the Coset Intersection Complex
Carolyn Abbott, Eduardo Martínez-Pedroza
For a pair consisting of a group and finite collection of subgroups, we introduce a simplicial -complex called the coset intersect…