20 citations · 50 across the 13 of their papers we have counts for
14 papers
Quasi-isometric rigidity of the integers: an elementary primer
Tarik Aougab, Hikaru Jitsukawa, Kim Ruane
Chatawate (Flame) Ruethaimetapat was a passionate, enthusiastic, and wonderful person who passed away in August of 2024. At the time of their passing they were working towards thei…
Local Connectivity of Right-angled Coxeter group boundaries
Michael Mihalik, Kim Ruane, Steve Tschantz
We provide conditions on the defining graph of a right-angled Coxeter group presentation that guarantees the boundary of any CAT(0) space on which the group acts geometrically will…
Hyperbolic groups and local connectivity
G. Christopher Hruska, Kim Ruane
The goal of this paper is to give an exposition of some results of Bestvina-Mess on local connectivity of the boundary of a one-ended word hyperbolic group. We also give elementary…
The boundary rigidity of lattices in products of trees
Kasia Jankiewicz, Annette Karrer, Kim Ruane +1
We show that every group acting freely and vertex-transitively by isometries on a product of two regular trees of finite valence is boundary rigid. That means that every CAT(0) spa…
An introduction to semistability in geometric group theory
G. Christopher Hruska, Kim Ruane
A finitely presented group is semistable at infinity if all proper rays in the Cayley 2-complex are properly homotopic. A long standing open question asks whether all finitely pres…
Connectedness properties and splittings of groups with isolated flats
G. Christopher Hruska, Kim Ruane
In this paper we study CAT(0) groups and their splittings as graphs of groups. For one-ended CAT(0) groups with isolated flats we prove a theorem characterizing exactly when the vi…