9 citations · 40 across the 22 of their papers we have counts for
8 papers · 1 filter
Extensions of hyperbolic groups have locally uniform exponential growth
Robert Kropholler, Rylee Alanza Lyman, Thomas Ng
We introduce a quantitative characterization of subgroup alternatives modeled on the Tits alternative in terms of group laws and investigate when this property is preserved under e…
Homological Dehn functions of groups of type
Noel Brady, Robert Kropholler, Ignat Soroko
We prove foundational results for homological Dehn functions of groups of type such as superadditivity and the invariance under quasi-isometry. We then study the homological…
Folding-like techniques for CAT(0) cube complexes
Michael Ben-Zvi, Robert Kropholler, Rylee Alanza Lyman
In a seminal paper, Stallings introduced folding of morphisms of graphs. One consequence of folding is the representation of finitely-generated subgroups of a finite-rank free grou…
A coarse embedding theorem for homological filling functions
Robert Kropholler, Mark Pengitore
We demonstrate under appropriate finiteness conditions that a coarse embedding induces an inequality of homological Dehn functions. Applications of the main results include a chara…
Finitely generated groups acting uniformly properly on hyperbolic space
Robert Kropholler, Vladimir Vankov
We construct an uncountable sequence of groups acting uniformly properly on hyperbolic spaces. We show that only countably many of these groups can be virtually torsion-free. This…
Incoherence of free-by-free and surface-by-free groups
Robert Kropholler, Stefano Vidussi, Genevieve Walsh
Let be the semidirect product where is either the free group , or the fundamental group of a closed surface of genus . We prove tha…
Medium-scale curvature at larger radii in finitely generated groups
Robert Kropholler, Brendan Mallery
In this paper we study medium scale curvature, a notion of Ricci curvature for groups. We show that dead-end elements yield non-negative curvature. We make use of related elements…
Betti numbers and coherence of random groups
Dawid Kielak, Robert Kropholler, Gareth Wilkes
We study Betti numbers, coherence, and virtual fibring of random groups in the few-relator model. In particular, random groups with negative Euler characteristic are coher…