Appears in collection : 2024 - T2 - WS1 - Low Dimensional Actions

Can any pair of commuting diffeomorphisms of a compact 1D manifold be connected to the trivial pair (id,id) via a path of such pairs ? This question plays an important role in the classification of foliations of 3-manifolds by surfaces. It can be asked in any differentiability class, and we will see that the phenomena at play and the techniques involved to answer it highly depend on the regularity, focussing on a new result in the intermediate regularity $C^{1+ac}$ (where « ac » stands for « absolutely continuous).

Joint with Andrés Navas.