9 citations · 11 across the 9 of their papers we have counts for
17 papers
Pontryagin duality and sheaves of profinite modules
Gareth Wilkes
The well-known theory of Pontryagin duality provides a strong connection between the homology and cohomology theories of a profinite group in appropriate categories. A construction…
Relative extensions and cohomology of profinite groups
Gareth Wilkes
We construct a correspondence between the cohomology groups of a group relative to a family of subgroups $\famS$ and the classes of `relative extensions' of by abelian grou…
A sufficient condition for accessibility of pro- groups
Gareth Wilkes
We establish a sufficient condition for a finitely generated pro- group to be accessible in terms of finite generation of the module of ends.
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…
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.
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…
On accessibility for pro- groups
Gareth Wilkes
We define the notion of accessibility for a pro- group. We prove that finitely generated pro- groups are accessible given a bound on the size of their finite subgroups. We th…
A criterion for residual -finiteness of arbitrary graphs of finite -groups
Gareth Wilkes
We establish conditions under which the fundamental group of a graph of finite -groups is necessarily residually -finite. The technique of proof is independent of previously…
Profinite completions, cohomology and JSJ decompositions of compact 3-manifolds
Gareth Wilkes
In this paper we extend previous results concerning the behaviour of JSJ decompositions of closed 3-manifolds with respect to the profinite completion to the case of compact 3-mani…
Profinite rigidity of graph manifolds, II: knots and mapping classes
Gareth Wilkes
In this paper we study some consequences of the author's classification of graph manifolds by their profinite fundamental groups. In particular we study commensurability, the behav…
Classification of pro- PD pairs and the pro- curve complex
Gareth Wilkes
We classify pro- Poincaré duality pairs in dimension two. We then use this classification to build a pro- analogue of the curve complex and establish its basic properties. We…
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…
Virtual pro- properties of 3-manifold groups
Gareth Wilkes
We answer a question of Aschenbrenner and Friedl regarding virtual -efficiency for 3-manifold groups. We then study conjugacy -separability and prove results for Fuchsian gro…
Profinite rigidity of graph manifolds and JSJ decompositions of 3-manifolds
Gareth Wilkes
There has been much recent interest into those properties of a 3-manifold determined by the profinite completion of its fundamental group. In this paper we give readily computable…
Profinite properties of RAAGs and special groups
Robert Kropholler, Gareth Wilkes
In this paper we prove that RAAGs are distinguished from each other by their pro- completions for any choice of prime , and that RACGs are distinguished from each other by th…
Profinite rigidity for Seifert fibre spaces
Gareth Wilkes
An interesting question is whether two 3-manifolds can be distinguished by computing and comparing their collections of finite covers; more precisely, by the profinite completions…
On the structure of vertex cuts separating the ends of a graph
Gareth R. Wilkes
Dinits, Karzanov and Lomonosov showed that the minimal edge cuts of a finite graph have the structure of a cactus, a tree-like graph constructed from cycles. Evangelidou and Papaso…