Seminar Algebra and Geometry: Jean Fasel (Grenoble)

A^1-contractibility of Koras-Russell threefolds

In this talk, which is a joint work with Adrien Dubouloz, we will explain that the unstable homotopy category is unable to distinguish between the affine space of dimension 3 and the Koras-Russell threefolds of the first kind. We will first make some historical remarks and then spend some time to explain the basic features of the unstable homotopy category, in particular how to distinguish isomorphisms in some special cases. We will then proceed with the proof of the above claim.

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