4 citations · 8 across the 7 of their papers we have counts for
11 papers · 1 filter
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…
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…
The asymptotic behaviour of Heegaard genus
Marc Lackenby
Let M be a closed orientable 3-manifold with a negatively curved Riemannian metric. Let {M_i} be a collection of finite regular covers with degree d_i. (1) If the Heegaard genus of…
Heegaard splittings, the virtually Haken conjecture and Property tau
Marc Lackenby
We examine three key conjectures in 3-manifold theory: the virtually Haken conjecture, the positive virtual b_1 conjecture and the virtually fibred conjecture. We explore the inter…
The canonical decomposition of once-punctured torus bundles
Marc Lackenby
In this paper, we determine the canonical polyhedral decomposition of every hyperbolic once-punctured torus bundle over the circle. In fact, we show that the only ideal polyhedral…