4-dimensional 2-handlebodies and the conjecture of Gompf

Vortrag von Maksymilian Piotr Manko

Datum: 23.10.25  Zeit: 16.05 - 17.05  Raum: ETH HG G 43

While for dimension 3 and lower it is well-known that any compact smooth manifold admits a unique smooth structure, in dimension 4 this is no longer true, giving rise to 4-manifolds admitting multiple ones. The question is, in particular, open for the 4-sphere, wherein it is known as the smooth 4-dimensional Poincaré conjecture. In this talk I will focus on a particular subclass of 4-manifolds having only 0- 1- and 2-handles in their handle decompositions, and an analogous conjecture regarding their smooth structures posed by Gompf. After explaining all the background and presenting the problems and how they are related, I will briefly mention the current strategies to attack them.