Gareth Wilkes

activity

20132024

most citedProfinite properties of RAAGs and special groups

9 citations · 11 across the 9 of their papers we have counts for

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10 papers · 1 filter

math.GR2022

Relative extensions and cohomology of profinite groups

Gareth Wilkes

We construct a correspondence between the cohomology groups of a group $G$ relative to a family of subgroups $\famS$ and the classes of `relative extensions' of $G$ by abelian grou…

math.GR2020

A sufficient condition for accessibility of pro- $p$ groups

Gareth Wilkes

We establish a sufficient condition for a finitely generated pro- $p$ group to be accessible in terms of finite generation of the module of ends.

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.GR2019

Distinguishing crystallographic groups by their finite quotients

Paweł Piwek, David Popović, Gareth Wilkes

Using the computer algebra program GAP, we show that all crystallographic groups in dimensions at most 4 are distinguished from each other by their sets of finite quotients.

math.GR2019★ 1 cited

Virtually abelian quotients of random groups

Gareth Wilkes

It is well-known that random groups with at least as many relators as generators have vanishing first betti number with high probability. In this paper we extend this question and…

math.GR2018

On accessibility for pro- $p$ groups

Gareth Wilkes

We define the notion of accessibility for a pro- $p$ group. We prove that finitely generated pro- $p$ groups are accessible given a bound on the size of their finite subgroups. We th…

math.GR2018

A criterion for residual $p$ -finiteness of arbitrary graphs of finite $p$ -groups

Gareth Wilkes

We establish conditions under which the fundamental group of a graph of finite $p$ -groups is necessarily residually $p$ -finite. The technique of proof is independent of previously…

math.GR2017

Classification of pro- $p$ PD $^{2}$ pairs and the pro- $p$ curve complex

Gareth Wilkes

We classify pro- $p$ Poincaré duality pairs in dimension two. We then use this classification to build a pro- $p$ analogue of the curve complex and establish its basic properties. We…

math.GR2017

Relative cohomology theory for profinite groups

Gareth Wilkes

In this paper we define and develop the theory of the cohomology of a profinite group relative to a collection of closed subgroups. Having made the relevant definitions we establis…

math.GR2016

Virtual pro- $p$ properties of 3-manifold groups

Gareth Wilkes

We answer a question of Aschenbrenner and Friedl regarding virtual $p$ -efficiency for 3-manifold groups. We then study conjugacy $p$ -separability and prove results for Fuchsian gro…

Relative extensions and cohomology of profinite groups

A sufficient condition for accessibility of pro-p groups

ℓ2 Betti numbers and coherence of random groups

Distinguishing crystallographic groups by their finite quotients

Virtually abelian quotients of random groups

On accessibility for pro-p groups

A criterion for residual p-finiteness of arbitrary graphs of finite p-groups

Classification of pro-p PD2 pairs and the pro-p curve complex

Relative cohomology theory for profinite groups

Virtual pro-p properties of 3-manifold groups

A sufficient condition for accessibility of pro- $p$ groups

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

On accessibility for pro- $p$ groups

A criterion for residual $p$ -finiteness of arbitrary graphs of finite $p$ -groups

Classification of pro- $p$ PD $^{2}$ pairs and the pro- $p$ curve complex

Virtual pro- $p$ properties of 3-manifold groups