42 citations · 68 across the 9 of their papers we have counts for
13 papers
Connectivity of Coxeter group Morse boundaries
Matthew Cordes, Ivan Levcovitz
We study the connectivity of Morse boundaries of Coxeter groups. We define two conditions on the defining graph of a Coxeter group: wide-avoidant and wide-spherical-avoidant. We sh…
Foundations of geometric approximate group theory
Matthew Cordes, Tobias Hartnick, Vera Tonić
We develop the foundations of a geometric theory of countably-infinite approximate groups, extending work of Björklund and the second-named author. Our theory is based on the notio…
Regularity of Morse geodesics and growth of stable subgroups
Matthew Cordes, Jacob Russell, Davide Spriano +1
We prove that Morse local-to-global groups grow exponentially faster than their infinite index stable subgroups. This generalizes a result of Dahmani, Futer, and Wise in the contex…
An embedding of the Morse boundary in the Martin boundary
Matthew Cordes, Matthieu Dussaule, Ilya Gekhtman
We construct a one-to-one continuous map from the Morse boundary of a hierarchically hyperbolic group to its Martin boundary. This construction is based on deviation inequalities g…
Complete topological descriptions of certain Morse boundaries
Ruth Charney, Matthew Cordes, Alessandro Sisto
We study direct limits of embedded Cantor sets and embedded \sier curves. We show that under appropriate conditions on the embeddings, all limits of Cantor spaces give rise to home…
Cannon--Thurston maps for CAT(0) groups with isolated flats
Benjamin Beeker, Matthew Cordes, Giles Gardam +2
Mahan Mitra (Mj) proved Cannon--Thurston maps exist for normal hyperbolic subgroups of a hyperbolic group. We prove that Cannon--Thurston maps do not exist for infinite normal hype…
Quasi-Mobius Homeomorphisms of Morse boundaries
Ruth Charney, Matthew Cordes, Devin Murray
The Morse boundary of a proper geodesic metric space is designed to encode hypberbolic-like behavior in the space. A key property of this boundary is that a quasi-isometry between…
A survey on Morse boundaries & stability
Matthew Cordes
In this paper we survey many of the known results about Morse boundaries and stability.
Relatively hyperbolic groups with fixed peripherals
Matthew Cordes, David Hume
We build quasi--isometry invariants of relatively hyperbolic groups which detect the hyperbolic parts of the group; these are variations of the stable dimension constructions previ…
Boundary convex cocompactness and stability of subgroups of finitely generated groups
Matthew Cordes, Matthew Gentry Durham
A Kleinian group is called convex cocompact if any orbit of in is quasiconvex or, equivalently, acts cocompactly on the convex…
Stability and the Morse boundary
Matthew Cordes, David Hume
Stable subgroups and the Morse boundary are two systematic approaches to collect and study the hyperbolic aspects of finitely generated groups. In this paper we unify and generaliz…
Random nilpotent groups I
Matthew Cordes, Moon Duchin, Yen Duong +2
We study random nilpotent groups in the well-established style of random groups, by choosing relators uniformly among freely reduced words of (nearly) equal length and letting the…
Morse Boundaries of Proper Geodesic Metric Spaces
Matthew Cordes
We introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with rays that identify the "hyperbolic directions" in that space. Th…