Colloquium
3:00 p.m., Friday (Jan. 17th)
Math Annex 1100
Nathan Dunfield
Harvard University
Surfaces in finite covers of 3manifolds:
The virtual Haken conjecture
Haken 3manifolds are those that contain topologically essential
embedded surfaces. Haken manifolds are very well understood and
most of the important questions in 3manifold topology and
geometry have been answered in this case. However, there are
many 3manifolds which are not Haken. For a nonHaken 3manifold
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).
