Not offered 2007-2008
MATH 426 Hyperbolic 3-Manifolds (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).
ADAMS