A problem coming independently arising from 1-dimensional dynamics and codimension-1 foliations asks whether the space of commuting circle or interval diffeomorphisms is path connected. This  is a very difficult question, with only partial results in very specific regularities. In this talk I will develop on recent work with Hélène Eynard.Bontemps (Inst. Fourier, Grenoble), where we prove path-connectedness in class C^{1+ac} and connectedness in class C^2 (C^{1+ac} stands for diffeomorphisms with absolutely continuous derivative).

https://indico.math.cnrs.fr/event/10089/