Finite covering spaces of 3-manifolds

@inproceedings{Lackenby2011FiniteCS,
  title={Finite covering spaces of 3-manifolds},
  author={Marc Lackenby},
  year={2011}
}
Following Perelman's solution to the Geometrisation Conjecture, a 'generic' closed 3-manifold is known to admit a hyperbolic structure. However, our understand- ing of closed hyperbolic 3-manifolds is far from complete. In particular, the notorious Virtually Haken Conjecture remains unresolved. This proposes that every closed hyper- bolic 3-manifold has a finite cover that contains a closed embedded orientable �1-injective surface with positive genus. I will give a survey on the progress… 
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TLDR
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