
As a companion to Freedman's lectures I will describe applications of the disk theorem to finding smooth structures on topological 4-manifolds, isotopy of homeomorphisms to be diffeomorphisms on various types of open sets, etc. One consequence is that handlebody structures are equivalent to smooth structures, so generally don't exist. I describe modifications of standard handlebody arguments to work around this problem.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/158