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Connectedness and deformation by conjugation of actions on [0,1] (or $^1)

By Hélène Eynard-Bontemps

Appears in collection : Big Mapping Class Groups and Diffeomorphism Groups / Gros groupes modulaires et groupes de difféomorphismes

The study of the path-connectedness of the space of $C^{r}$ actions of $\mathbb{Z}^{2}$ on the interval [0,1] plays an important role in the classification of codimension 1 foliations on 3 manifolds. One way to deform actions is by conjugation. If an action can be brought arbitrarily close to the trivial one by conjugation, it is said to be quasi-reducible. In this talk, we will present and compare obstructions to quasi-reducibility in different regularity classes, and draw conclusions concerning the initial connectedness problem.

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Citation data

  • DOI 10.24350/CIRM.V.19968003
  • Cite this video Eynard-Bontemps Hélène (10/10/22). Connectedness and deformation by conjugation of actions on [0,1] (or $^1). CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19968003
  • URL https://dx.doi.org/10.24350/CIRM.V.19968003


  • EYNARD-BONTEMPS, Hélène et NAVAS, Andrés. Arc-connectedness for the space of smooth $\mathbb {Z}^ d $-actions on 1-dimensional manifolds. arXiv preprint arXiv:2103.06940, 2021. - https://doi.org/10.48550/arXiv.1209.1601
  • EYNARD-BONTEMPS, Hélène et NAVAS, Andrés. Mather invariant, distortion, and conjugates for diffeomorphisms of the interval. Journal of Functional Analysis, 2021, vol. 281, no 9, p. 109149. - https://doi.org/10.1016/j.jfa.2021.109149

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