Program
François Laudenbach (Nantes)
Title:
A foliated proof of Γ4 = 0
Abstract:
This cryptic title names a famous theorem proved by Jean Cerf in the late sixties. It states that every diffeomorphism of the 3-dimensional sphere extends to the 4-ball.
The actual 1968 theorem of Cerf states that every orientation preserving diffeomorphism of the 3-sphere is isotopic to the identity, and hence Γ4 = 0 as an immediate corollary.
In his 1992 article to the memory of Claude Godbillon and Jean Martinet, Yakov Eliashberg gave a proof of Γ4 = 0 using the tools of the time in contact geometry and pseudo holomorphic curves, without passing through the above-mentioned connectivity of Diff+S3.
In this talk, I would like to explain the proof that I recently wrote of Cerf’s 1968 theorem. This immediately reduces to an isotopy theorem for foliations of S2 × [0, 1] tangent to the boundary. Surprisingly enough, this geometric setup is easy to deal with. The key relies on a convenient series of Dehn’s surgeries which kills all evident obstructions without changing the initial isotopy problem.