7 papers
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…
Graphs and complexes of lattices
Sam Hughes
We study lattices acting on spaces via their commensurated subgroups. To do this we introduce the notions of a graph of lattices and a complex of lattices giving…
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…
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…
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 is a free-by-cyclic group with…
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…