Virtually fibered conjecture

In the mathematical subfield of 3-manifolds, the virtually fibered conjecture, formulated by American mathematician William Thurston, states that every closed, irreducible, atoroidal 3-manifold with infinite fundamental group has a finite cover which is a surface bundle over the circle.

In a posting on the ArXiv on 25 Aug 2009,[2] Daniel Wise implicitly implied (by referring to a then-unpublished longer manuscript) that he had proven the conjecture for the case where the 3-manifold is closed, hyperbolic, and Haken.

This was followed by a survey article in Electronic Research Announcements in Mathematical Sciences.

[7] In March 2012, during a conference at Institut Henri Poincaré in Paris, Ian Agol announced he could prove the virtually Haken conjecture for closed hyperbolic 3-manifolds .

[8] Taken together with Daniel Wise's results, this implies the virtually fibered conjecture for all closed hyperbolic 3-manifolds.