Robert P. Kropholler

activity

20152025

most citedProfinite properties of RAAGs and special groups

9 citations · 40 across the 22 of their papers we have counts for

collaborators

27 papers

math.GR2025

Explicit polynomial bounds on Dehn functions of subgroups of hyperbolic groups

Robert Kropholler, Claudio Llosa Isenrich, Ignat Soroko

In 1999 Brady constructed the first example of a non-hyperbolic finitely presented subgroup of a hyperbolic group by fibring a non-positively curved cube complex over the circle. W…

math.GR2024

Subgroups of word hyperbolic groups in dimension 2 over arbitrary rings

Shaked Bader, Robert Kropholler, Vladimir Vankov

In 1996, Gersten proved that finitely presented subgroups of a word hyperbolic group of integral cohomological dimension 2 are hyperbolic. We use isoperimetric inequalities over ar…

math.GR2023

Finitely presented kernels of homomorphisms from hyperbolic groups onto free abelian groups

Robert Kropholler, Claudio Llosa Isenrich

For every $m \geq 2$ we produce an example of a non-hyperbolic finitely presented subgroup $H < G$ of a hyperbolic group $G$ , which is the kernel of a surjective homomorphism $ϕ: G\…

math.GT2021

Virtual algebraic fibrations of surface-by-surface groups and orbits of the mapping class group

Robert Kropholler, Stefano Vidussi, Genevieve Walsh

We show that a conjecture of Putman--Wieland, which posits the nonexistence of finite orbits for higher Prym representations of the mapping class group, is equivalent to the existe…

math.GR2021

Dehn functions of coabelian subgroups of direct products of groups

Robert Kropholler, Claudio Llosa Isenrich

We develop new methods for computing the precise Dehn functions of coabelian subgroups of direct products of groups, that is, subgroups which arise as kernels of homomorphisms from…

math.GR2021

Constructing groups of type $F P_{2}$ over fields but not over the integers

Robert Kropholler

We construct examples of groups that are $F P_{2} (Q)$ and $F P_{2} (Z / p Z)$ for all primes $p$ but not of type $F P_{2} (Z)$ .

math.GR2020★ 1 cited

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…

math.GR2020★ 3 cited

Homological Dehn functions of groups of type $F P_{2}$

Noel Brady, Robert Kropholler, Ignat Soroko

We prove foundational results for homological Dehn functions of groups of type $F P_{2}$ such as superadditivity and the invariance under quasi-isometry. We then study the homological…

math.GR2020★ 3 cited

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…

math.GT2020

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…

math.GR2020

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…

math.GR2020

Incoherence of free-by-free and surface-by-free groups

Robert Kropholler, Stefano Vidussi, Genevieve Walsh

Let $G$ be the semidirect product $Γ ⋊ F_{2}$ where $Γ$ is either the free group $F_{n}$ , $n > 1$ or the fundamental group $S_{g}$ of a closed surface of genus $g > 1$ . We prove tha…

math.GR2020★ 4 cited

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…

math.GR2020

$ℓ^{2}$ Betti numbers and coherence of random groups

Dawid Kielak, Robert Kropholler, Gareth Wilkes

We study $ℓ^{2}$ Betti numbers, coherence, and virtual fibring of random groups in the few-relator model. In particular, random groups with negative Euler characteristic are coher…

math.GT2019

Groups with arbitrary cubical dimension gap

Robert Kropholler, Chris O'Donnell

We prove that if $G = G_{1} \times \dots \times G_{n}$ acts essentially, properly and cocompactly on a CAT(0) cube complex X, then the cube complex splits as a product. We use this theore…

math.GR2019

Right-angled Artin group boundaries

Michael Ben-Zvi, Robert Kropholler

In all known examples of a CAT(0) group acting on CAT(0) spaces with non-homeomorphic CAT(0) visual boundaries, the boundaries are each not path connected. In this paper, we show t…

math.GR2019

Incoherence and fibering of many free-by-free groups

Robert Kropholler, Genevieve Walsh

We show that free-by-free groups satisfying a homological criterion, which we call excessive homology, are incoherent. This class is large in nature, including many examples of hyp…

math.GR2018★ 4 cited

Hyperbolic groups with almost finitely presented subgroups

Robert Kropholler, Federico Vigolo

In this paper we create many examples of hyperbolic groups with subgroups satisfying interesting finiteness properties. We give the first examples of subgroups of hyperbolic groups…

math.GR2018

Hyperbolic Groups with Finitely Presented Subgroups not of Type $F_{3}$

Robert Kropholler, Giles Gardam

We generalise the constructions of Brady and Lodha to give infinite families of hyperbolic groups, each having a finitely presented subgroup that is not of type $F_{3}$ . By calculati…

math.GR2018

Groups whose word problems are not semilinear

Robert H. Gilman, Robert P. Kropholler, Saul Schleimer

Suppose that G is a finitely generated group and W is the formal language of words defining the identity in G. We prove that if G is a nilpotent group, the fundamental group of a f…

math.GR2018★ 4 cited

Almost Hyperbolic Groups with Almost Finitely Presented Subgroups

Robert Kropholler

We construct new examples of CAT(0) groups containing non finitely presented subgroups that are of type $F P_{2}$ , these CAT(0) groups do not contain copies of $Z^{3}$ . We also…

math.MG2018★ 3 cited

A new construction of CAT(0) cube complexes

Robert Kropholler, Federico Vigolo

We introduce the notion of coupled link cube complex (CLCC) as a means of constructing interesting cocompactly cubulated groups. CLCCs are defined locally, making them a useful too…

math.GR2017★ 4 cited

Uncountably many quasi-isometry classes of groups of type $F P$

Robert P Kropholler, Ian J Leary, Ignat Soroko

Previously one of the authors constructed uncountable families of groups of type $F P$ and of $n$ -dimensional Poincaré duality groups for each $n \geq 4$ . We strengthen these results…

math.GR2017

Conjugation curvature for Cayley graphs

Assaf Bar-Natan, Moon Duchin, Robert Kropholler

We introduce a notion of Ricci curvature for Cayley graphs that can be thought of as "medium-scale" because it is neither infinitesimal nor asymptotic, but based on a chosen finite…

Explicit polynomial bounds on Dehn functions of subgroups of hyperbolic groups

Subgroups of word hyperbolic groups in dimension 2 over arbitrary rings

Finitely presented kernels of homomorphisms from hyperbolic groups onto free abelian groups

Virtual algebraic fibrations of surface-by-surface groups and orbits of the mapping class group

Dehn functions of coabelian subgroups of direct products of groups

Constructing groups of type FP2​ over fields but not over the integers

Extensions of hyperbolic groups have locally uniform exponential growth

Homological Dehn functions of groups of type FP2​

Folding-like techniques for CAT(0) cube complexes

A coarse embedding theorem for homological filling functions

Finitely generated groups acting uniformly properly on hyperbolic space

Incoherence of free-by-free and surface-by-free groups

Medium-scale curvature at larger radii in finitely generated groups

ℓ2 Betti numbers and coherence of random groups

Groups with arbitrary cubical dimension gap

Right-angled Artin group boundaries

Incoherence and fibering of many free-by-free groups

Hyperbolic groups with almost finitely presented subgroups

Hyperbolic Groups with Finitely Presented Subgroups not of Type F3​

Groups whose word problems are not semilinear

Almost Hyperbolic Groups with Almost Finitely Presented Subgroups

A new construction of CAT(0) cube complexes

Uncountably many quasi-isometry classes of groups of type FP

Conjugation curvature for Cayley graphs

Constructing groups of type $F P_{2}$ over fields but not over the integers

Homological Dehn functions of groups of type $F P_{2}$

$ℓ^{2}$ Betti numbers and coherence of random groups

Hyperbolic Groups with Finitely Presented Subgroups not of Type $F_{3}$

Uncountably many quasi-isometry classes of groups of type $F P$