4 papers
Gromov boundary of the Grand Arc graph
Carolyn Abbott, Assaf Bar-Natan, Arya Vadnere
We describe a dense subset of the Gromov boundary of the grand arc graph of an infinite-type surface as a space of geodesic laminations, analogous to Klarreich's description of the…
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…