Sam Hughes

activity

20182026

most citedLattices in a product of trees, hierarchically hyperbolic groups, and virtual torsion-freeness

9 citations · 53 across the 22 of their papers we have counts for

collaborators

25 papers

math.GR2026

Outer automorphisms of HNN extensions of abelian groups

Naomi Andrew, Sam Hughes, Motiejus Valiunas

Let $G$ be a commensurating HNN extension of a finitely generated free abelian group. We characterise when $Out (G)$ is finitely generated and derive structural information…

math.GR2026

Spherical and affine Artin groups, finite quotients, and the isomorphism problem

Sam Hughes, Thomas Ng, Kaitlin Ragosta +2

We compute the smallest non-abelian quotients of spherical and affine Artin groups. Usually, these are isomorphic to the smallest non-abelian quotients of the corresponding Coxeter…

math.AT2026

Some closed manifolds that do not fibre over the circle

Sam Hughes, Ian Leary, Wolfgang Lueck

We construct closed manifolds with vanishing L^2-Betti numbers over every field) which do not virtually fibre over the circle. The class of fundamental groups that occurs is the la…

math.GR2023

Centralisers and the virtually cyclic dimension of $Out (F_{N})$

Yassine Guerch, Sam Hughes, Luis Jorge Sánchez Saldaña

We prove that the virtually cyclic (geometric) dimension of the finite index congruence subgroup $IA_{N} (3)$ of $Out (F_{N})$ is $2 N - 2$ . From this we deduce the virtua…

math.GR2023★ 1 cited

Homology growth of polynomially growing mapping tori

Naomi Andrew, Yassine Guerch, Sam Hughes +1

We prove that residually finite mapping tori of polynomially growing automorphisms of hyperbolic groups, groups hyperbolic relative to finitely many virtually polycyclic groups, ri…

math.GR2023

A note on asynchronously automatic groups and notions of non-positive curvature

Sam Hughes, Motiejus Valiunas

We prove groups acting cocompactly on locally finite trees with hyperbolic vertex stabilisers are asynchronously automatic. Combining this with previous work of the authors, we obt…

math.GR2023★ 1 cited

On profinite rigidity amongst free-by-cyclic groups I: the generic case

Sam Hughes, Monika Kudlinska

We prove that amongst the class of free-by-cyclic groups, Gromov hyperbolicity is an invariant of the profinite completion. We show that whenever $G$ is a free-by-cyclic group with…

math.GR2023

Coherence for elementary amenable groups

Sam Hughes, Dawid Kielak, Peter H. Kropholler +1

We prove that for an elementary amenable group, coherence of the group, homological coherence of the group, and coherence of the integral group ring are all equivalent. This genera…

math.GR2022★ 4 cited

Homological growth of Artin kernels in positive characteristic

Sam P. Fisher, Sam Hughes, Ian J. Leary

We prove an analogue of the Lück Approximation Theorem in positive characteristic for certain residually finite rationally soluble (RFRS) groups including right-angled Artin groups…

math.GR2022★ 5 cited

Torsion homology growth of polynomially growing free-by-cyclic groups

Naomi Andrew, Sam Hughes, Monika Kudlinska

We show that the homology torsion growth of a free-by-cyclic group with polynomially growing monodromy vanishes in every dimension independently of the choice of Farber chain. It f…

math.GR2022★ 2 cited

Profinite rigidity of fibring

Sam Hughes, Dawid Kielak

We introduce the classes of TAP groups, in which various types of algebraic fibring are detected by the non-vanishing of twisted Alexander polynomials. We show that finitely presen…

math.GR2022★ 3 cited

Regularity of quasigeodesics characterises hyperbolicity

Sam Hughes, Patrick S. Nairne, Davide Spriano

We characterise hyperbolic groups in terms of quasigeodesics in the Cayley graph forming regular languages. We also obtain a quantitative characterisation of hyperbolicity of geode…

math.KT2022

A note on the rational homological dimension of lattices in positive characteristic

Sam Hughes

We show via $ℓ^{2}$ -homology that the rational homological dimension of a lattice in a product of simple simply connected Chevalley groups over global function fields is equal to…

math.GR2022★ 5 cited

Commensurating HNN-extensions: hierarchical hyperbolicity and biautomaticity

Sam Hughes, Motiejus Valiunas

We construct a CAT(0) hierarchically hyperbolic group (HHG) acting geometrically on the product of a hyperbolic plane and a locally-finite tree which is not biautomatic. This gives…

math.GR2022★ 2 cited

Hyperbolically embedded subgroups and quasi-isometries of pairs

Sam Hughes, Eduardo Martínez-Pedroza

We give technical conditions for a quasi-isometry of pairs to preserve a subgroup being hyperbolically embedded. We consider applications to the quasi-isometry and commensurability…

math.GR2022

Irreducible lattices fibring over the circle

Sam Hughes

We investigate the Bieri--Neumann--Strebel--Renz (BNSR) invariants of irreducible uniform lattices. In the case of a direct product of a tree and a Euclidean space we show that van…

math.GR2021★ 2 cited

A survey on quasi-isometries of pairs: invariants and rigidity

Sam Hughes, Eduardo Martínez-Pedroza, Luis Jorge Sánchez Saldaña

This survey studies pairs $(G, P)$ with $G$ a finitely generated group and $P$ a (finite) collection of subgroups of $G$ . We explore the notion of quasi-isometry…

math.AT2021★ 2 cited

Higher topological complexity of hyperbolic groups

Sam Hughes, Kevin Li

We prove for non-elementary torsion-free hyperbolic groups $Γ$ and all $r \geq 2$ that the higher topological complexity $TC_{r} (Γ)$ is equal to $r \cdot cd (Γ)$ . In part…

math.GR2021★ 3 cited

Quasi-isometry invariance of relative filling functions

Sam Hughes, Eduardo Martínez-Pedroza, Luis Jorge Sánchez Saldaña

For a finitely generated group $G$ and collection of subgroups $P$ we prove that the relative Dehn function of a pair $(G, P)$ is invariant under quasi-isometry…

math.GR2021★ 9 cited

Lattices in a product of trees, hierarchically hyperbolic groups, and virtual torsion-freeness

Sam Hughes

We construct cocompact lattices in a product of trees which are not virtually torsion-free. This gives the first examples of hierarchically hyperbolic groups which are not virtuall…

math.GR2021★ 7 cited

Graphs and complexes of lattices

Sam Hughes

We study lattices acting on $CAT (0)$ spaces via their commensurated subgroups. To do this we introduce the notions of a graph of lattices and a complex of lattices giving…

math.GR2020★ 1 cited

The first $ℓ^{2}$ -Betti number and groups acting on trees

Indira Chatterji, Sam Hughes, Peter Kropholler

We generalise results of Thomas, Allcock, Thom-Petersen, and Kar-Niblo to the first $ℓ^{2}$ -Betti number of quotients of certain groups acting on trees by subgroups with free acti…

math.KT2020★ 2 cited

On the equivariant $K$ - and $K O$ -homology of some special linear groups

Sam Hughes

We compute the equivariant $K O$ -homology of the classifying space for proper actions of $SL_{3} (Z)$ and $GL_{3} (Z)$ . We also compute the Bredon homo…

math.GR2019★ 4 cited

Cohomology of Fuchsian Groups and Non-Euclidean Crystallographic Groups

Sam Hughes

For each geometrically finite 2-dimensional non-Euclidean crystallographic group (NEC group), we compute the cohomology groups. In the case where the group is a Fuchsian group, we…

Outer automorphisms of HNN extensions of abelian groups

Spherical and affine Artin groups, finite quotients, and the isomorphism problem

Some closed manifolds that do not fibre over the circle

Centralisers and the virtually cyclic dimension of Out(FN​)

Homology growth of polynomially growing mapping tori

A note on asynchronously automatic groups and notions of non-positive curvature

On profinite rigidity amongst free-by-cyclic groups I: the generic case

Coherence for elementary amenable groups

Homological growth of Artin kernels in positive characteristic

Torsion homology growth of polynomially growing free-by-cyclic groups

Profinite rigidity of fibring

Regularity of quasigeodesics characterises hyperbolicity

A note on the rational homological dimension of lattices in positive characteristic

Commensurating HNN-extensions: hierarchical hyperbolicity and biautomaticity

Hyperbolically embedded subgroups and quasi-isometries of pairs

Irreducible lattices fibring over the circle

A survey on quasi-isometries of pairs: invariants and rigidity

Higher topological complexity of hyperbolic groups

Quasi-isometry invariance of relative filling functions

Lattices in a product of trees, hierarchically hyperbolic groups, and virtual torsion-freeness

Graphs and complexes of lattices

The first ℓ2-Betti number and groups acting on trees

On the equivariant K- and KO-homology of some special linear groups

Cohomology of Fuchsian Groups and Non-Euclidean Crystallographic Groups

Centralisers and the virtually cyclic dimension of $Out (F_{N})$

The first $ℓ^{2}$ -Betti number and groups acting on trees

On the equivariant $K$ - and $K O$ -homology of some special linear groups