MATHEMATICS COLLOQUIUM - Mark Powell (Faculty Candidate)

Speaker: 
Mark Powell (Indiana University, Bloomington)
Topic: 
A Filtration of Topologically Slice Links

Abstract: A link in the 3-sphere is slice if its components bound a collection of disjointly embedded disks in the 4-ball.  In the topological category, the disks are required to be locally flat; in the smooth category they must be smooth embeddings.  The latter is a stronger condition, and there has been much interest in the differences between the two categories, the first of which were revealed by Donaldson and Freedman in the early 1980s.  In joint work with Jae Choon Cha, we showed that a filtration of the set of topologically slice links modulo smoothly slice links is nontrivial at every stage, and indeed once a suitable group structure is arranged, the associated quotients are infinitely generated.  The filtration, which is due to Tim Cochran, Shelly Harvey and Peter Horn, gives a framework for organising our knowledge about the difference in categories.  I will describe some of the ideas involved, with plenty of pictures.

Event Date: 
January 29, 2014 - 3:30pm to 4:30pm
Location: 
213 MLH
Calendar Category: 
Colloquium