Jean-Claude Hausmann (Geneva)

Title:

Differentiable rigidity : André Haefliger's contribution

Abstract:

We present Haefliger's works on the space of smooth embedings from the sphere Sⁿ into the Euclidean space R^m (1960-62). He first prove that there is only one smooth isotopy class when 3n+3 < 2m (metastable range). But, when 3n+3 = 2m, Haefliger, using completely different mathematics, found embeddings (e.g. from S³ into R⁶) which are not smoothly isotopic, though they are topologically isotopic by a theorem of Zeeman. Such a differentiable rigidity for smooth embeddings (after that of diffeomorphisms, discovered by Milnor) was unexpected and has been quite a surprise at the time.