Surfaces in finite covers of 3-manifolds: The virtual Haken conjecture

Haken 3-manifolds are those that contain topologically essential embedded surfaces. Haken manifolds are very well understood and most of the important questions in 3-manifold topology and geometry have been answered in this case. However, there are many 3-manifolds which are not Haken. For a non-Haken 3-manifold with infinite fundamental group, one can ask if it has a finite cover which is Haken. That such a manifold should always have such a cover is the virtual Haken conjecture. I will broadly survey recent progress towards, and evidence for, this conjecture, after first giving some idea of why Haken manifolds are so "easy" to understand.

Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).