I will explain what the validity of surgery in dimension 4 would imply about groups (mostly free groups) acting on the 3-sphere, and describe some interesting examples of such actions.
This is an expository talk about some stuff (mostly due to Freedman) from the 1980's.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/TopologySeminar