3:00 p.m., Friday (Jan. 17th)
Math Annex 1100
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"
Refreshments will be served at 2:45 p.m. in the Faculty Lounge,
Math Annex (Room 1115).