33 citations · 168 across the 48 of their papers we have counts for
5 papers · 1 filter
Adding high powered relations to large groups
Marc Lackenby
A group is known as `large' if some finite index subgroup admits a surjective homomorphism onto a non-abelian free group. The main theorem of the paper is as follows. Let G be a fi…
New lower bounds on subgroup growth and homology growth
Marc Lackenby
We establish new strong lower bounds on the (subnormal) subgroup growth of a large class of groups. This includes the fundamental groups of all finite-volume hyperbolic 3-manifolds…
Large groups, Property (tau) and the homology growth of subgroups
Marc Lackenby
We investigate the homology of finite index subgroups G_i of a given finitely presented group G. Specifically, we examine d_p(G_i), which is the dimension of the first homology of…
Covering spaces of 3-orbifolds
Marc Lackenby
Let O be a compact orientable 3-orbifold with non-empty singular locus and a finite volume hyperbolic structure. (Equivalently, O is the quotient of hyperbolic 3-space by a lattice…
Some 3-manifolds and 3-orbifolds with large fundamental group
Marc Lackenby
We provide two new proofs of a theorem of Cooper, Long and Reid which asserts that, apart from an explicit finite list of exceptional manifolds, any compact orientable irreducible…