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.