Adrien Dubouloz (Bourgogne): Families of A1-contractible affine threefolds
The so-called Koras-Russell threefolds are a family of topologically contractible rational smooth complex affine threefolds which played an important role in the linearization problem for multiplicative group actions on the affine 3-space. They are known to be all diffeomorphic to the 6-dimensional Euclidean space, but it was shown by Makar-Limanov in the nineties that none of them are algebraically isomorphic to the affine 3-space. It is however not known whether they are stably isomorphic or not to an affine space. Recently, Hoyois, Krishna and Østvær proved that many of these varieties become contractible in the unstable 𝔸1-homotopy category of Morel and Voevodsky after some finite suspension with the pointed projective line. In this talk, I will explain how additional geometric properties related to additive group actions on such varieties allow to conclude that a large class of them are actually 𝔸1-contractible (Joint work with Jean Fasel, Université Grenoble-Alpes).