5 citations · 10 across the 6 of their papers we have counts for
14 papers
Constructing groups of type over fields but not over the integers
Robert Kropholler
We construct examples of groups that are and for all primes but not of type .
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…
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…
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…