4 citations · 8 across the 7 of their papers we have counts for
14 papers
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…
A characterisation of large finitely presented groups
Marc Lackenby
A group is known as `large' if some finite index subgroup admits a surjective homomorphism onto a non-abelian free group. In this paper, we give a necessary and sufficient conditio…
Expanders, rank and graphs of groups
Marc Lackenby
Let G be a finitely presented group, and let {G_i} be a collection of finite index normal subgroups that is closed under intersections. Then, we prove that at least one of the foll…
The Heegaard genus of amalgamated 3-manifolds
Marc Lackenby
Let M and M' be simple 3-manifolds, each with connected boundary of genus at least two. Suppose that M and M' are glued via a homeomorphism between their boundaries. Then we show t…