This just in: Ian Agol (UC Berkeley), speaking at the Institut Henri Poincaré today, has announced a proof of the very same Wise’s Conjecture that I blogged about just last week! In particular, this implies the Virtually Haken Conjecture. His proof is based on joint work with Daniel Groves (UI Chicago) and Jason Manning (SUNY Buffalo). It makes heavy use of the work of Dani Wise (McGill) on the Virtually Fibred Conjecture, as well as the proof of the Surface Subgroup Conjecture by Jeremy Kahn (Brown) and Vlad Markovic (Caltech).
Of course, to get the statement on the blackboard, you also have to invoke Perelman’s proof of Geometrization.
For the suspicious, I did not know about this when I blogged last week. Thanks to Stefan Friedl (Köln) for the news and the photo.