MATH 426 Hyperbolic 3-Manifolds (Not offered 2006-2007; to be offered 2007-2008) (Q)
3-manifolds are objects that locally look 3-dimensional, the spatial universe
being an excellent example. For the last 100 years, mathematicians have tried to
determine all the possible 3-manifolds and means for distinguishing between
them. In 1978, William Thurston stated the Geometrization Conjecture, which
essentially says that any 3-manifold can be cut into pieces, each of which has
one of eight geometries. The pieces with seven of the geometries have been
completely determined. But the pieces that have hyperbolic geometry, the
so-called hyperbolic 3-manifolds, remain unclassified. This is because here is
where all the action is, where the richest structure lies. Here is where geometry
collides with topology. In this course, we will investigate hyperbolic
3-manifolds, from their beginnings in 1978 to the current research going on
today.
Format: lecture. Evaluation will be based on problem sets, oral presentation and
exams.
Prerequisites: Mathematics 301 or Mathematics 323 or Mathematics 324 or,
with permission of instructor, any of Mathematics 305, 312, 315 or 321. No
enrollment limit (expected:12).