Mixed $3$-manifolds are virtually special

Mixed 3–manifolds Are Virtually Special

LetM be a compact oriented irreducible 3–manifold which is neither a graph manifold nor a hyperbolic manifold. We prove that π1M is virtually special.

Graph manifolds with boundary are virtually special

Let M be a graph manifold. We prove that fundamental groups of embedded incompressible surfaces in M are separable in π1M , and that the double cosets for crossing surfaces are also separable. We deduce that if there is a ‘sufficient’ collection of surfaces in M , then π1M is virtually the fundamental group of a special non-positively curved cube complex. We provide a sufficient collection for ...

Coxeter groups are virtually special

In this paper we prove that every finitely generated Coxeter group has a finite index subgroup that is the fundamental group of a special cube complex. Some consequences include: Every f.g. Coxeter group is virtually a subgroup of a right-angled Coxeter group. Every word-hyperbolic Coxeter group has separable quasiconvex subgroups. © 2010 Elsevier Inc. All rights reserved. MSC: 53C23; 20F36; 20...

Fibred and Virtually Fibred Hyperbolic 3-Manifolds in the Censuses

A Characterization of Virtually Embedded Subsurfaces in 3-manifolds

The paper introduces the spirality character of the almost fiber part for a closed essentially immersed subsurface of a closed orientable aspherical 3-manifold, which generalizes an invariant due to Rubinstein and Wang. The subsurface is virtually embedded if and only if the almost fiber part is aspiral, and in this case, the subsurface is virtually a leaf of a taut foliation. Besides other con...