# Finite covers of random 3-manifolds

@article{Dunfield2006FiniteCO, title={Finite covers of random 3-manifolds }, author={Nathan M. Dunfield and William P. Thurston}, journal={Inventiones mathematicae}, year={2006}, volume={166}, pages={457-521} }

A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. In this paper, we study random 3-manifolds and their finite covers in an attempt to shed light on this difficult question. In particular, we consider random Heegaard splittings by gluing two handlebodies by the result of a random walk in the mapping class group of a surface. For this model… CONTINUE READING

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