Browsing Department of Pure Mathematics and Mathematical Statistics (DPMMS) by Author "Wilton, Henry John"
Now showing items 1-7 of 7
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3-manifolds everywhere
Calegari, Danny; Wilton, Henry JohnA random group contains many subgroups which are isomorphic to the fundamental group of a compact hyperbolic 3-manifold with totally geodesic boundary. These subgroups can be taken to be quasi-isometrically embedded. This ...
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Distinguishing geometries using finite quotients
Wilton, Henry John; Zalesskii, P (Mathematical Sciences PublishersGeometry and Topology, 2017-02-10)We prove that the profinite completion of the fundamental group of a compact 3-manifold M satisfies a Tits alternative: if a closed subgroup H does not contain a free pro-p subgroup for any p, then H is virtually soluble, ...
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Pro-p subgroups of profinite completions of 3-manifold groups
Wilton, Henry John; Zalesskii, PWe completely describe the finitely generated pro-$p$ subgroups of the profinite completion of the fundamental group of an arbitrary 3-manifold. We also prove a pro-$p$ analogue of the main theorem of Bass–Serre theory for ...
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Stackings and the W-cycles conjecture
Louder, L; Wilton, Henry JohnWe prove Wise’s W-cycles conjecture: Consider a compact graph Γ′ immersing into another graph Γ. For any immersed cycle Λ : S¹ → Γ, we consider the map Λ′ from the circular components S of the pullback to Γ′. Unless Λ′ is ...
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The structure of limit groups over hyperbolic groups
Groves, Daniel; Wilton, Henry John
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The Triviality problem for profinite completions
Bridson, Martin R; Wilton, Henry John (SpringerInventiones Mathematicae, 2015-02-24)We prove that there is no algorithm that can determine whether or not a finitely presented group has a non-trivial finite quotient; indeed, this property remains undecidable among the fundamental groups of compact, ...
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Undecidability and the developability of permutoids and rigid pseudogroups
Bridson, MR; Wilton, Henry John (Cambridge University PressForum of Mathematics, Sigma, 2017-03-20)A $\textit{permutoid}$ is a set of partial permutations that contains the identity and is such that partial compositions, when defined, have at most one extension in the set. In 2004 Peter Cameron conjectured that there ...