University of Georgia
Mathematics Department Colloquium
Abby Thompson
University of California, Davis
February 4th 1999
Classifying knots and 3-manifolds
Abstract: A central problem in 3-dimensional topology is to classify
3-dimensional spaces. That is, given a collection of tetrahedra,
together with instructions on how to glue their faces together, we'd
like to be able to decide algorithmically what the resulting
3-dimensional space is. I'll discuss the classifcation theorem for
knots in the 3-sphere, its implications for the classification of
3-manifolds, and progress on the simplest case of the classification
problem for 3-manifolds.