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

Showing 2021Show all

5 papers · 1 filter

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…