(Virtual)
In dimension four, the differences between continuous and differential topology are vast but fundamentally unstable, disappearing when manifolds are enlarged in various ways (especially through connected sums with S2xS2). I will discuss Wall's stabilization problem and some of its variants, all of which aim to quantify the instability of exotic phenomena. Guided by a connection between Wall’s stabilization problem and the famous h-cobordism problem, I will outline an “atomic approach” to addressing these problems, providing a construction of exotic 4-dimensional phenomena that are candidates to survive any prescribed number of stabilizations.
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