Date: 7 February 2014, 4:30pm
Location: Hempfield High School, Room 213
 Speaker: Paul Melvin, Bryn Mawr College
   Title: Dissolution of 4-dimensional exoticity

Abstract.  

It is a well known principle in 4-dimensional topology that homeomorphic
smooth simply-connected 4-manifolds become diffeomorphic after
stabilizing, i.e. connected summing with S2xS2, sufficiently many times.
Although many explicit examples are known for which exactly one
stabilization is required, no examples have been shown to require more
than one.  Perhaps this exoticity 'dissolves' quickly under
stabilization.

An analogous principle holds for 2-spheres embedded in a
simply-connected 4-manifold, namely, any two that are topologically
isotopic become smoothly isotopic after stabilizing the manifold
sufficiently many times.  Until now, however, bounds on the number of
stabilizations needed have not been found for any examples.  In this
talk we will describe pairs of topologically isotopic knots that are not
smoothly isotopic, but become so after one stabilization.  This is joint
work with Dave Auckly, Hee Jung Kim and Danny Ruberman.