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Connectedness and deformation by conjugation of actions on [0,1] (or $^1)
Multi angle
Authors : Eynard-Bontemps, Hélène (Author of the conference)
CIRM (Publisher )
37C05 - Smooth mappings and diffeomorphisms
37C10 - Vector fields, flows, ordinary differential equations
37C15 - Topological and differentiable equivalence, conjugacy, invariants, moduli, classification
37E05 - Maps of the interval (piecewise continuous, continuous, smooth)
57S25 - Groups acting on specific manifolds
37E10 - Dynamical systems involving maps of the circle
CIRM (Publisher )
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Abstract :
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.
Keywords : one-dimensional dynamics; connectedness; Z^2-actions
MSC Codes : Keywords : one-dimensional dynamics; connectedness; Z^2-actions
37C05 - Smooth mappings and diffeomorphisms
37C10 - Vector fields, flows, ordinary differential equations
37C15 - Topological and differentiable equivalence, conjugacy, invariants, moduli, classification
37E05 - Maps of the interval (piecewise continuous, continuous, smooth)
57S25 - Groups acting on specific manifolds
37E10 - Dynamical systems involving maps of the circle
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 14/11/2022 Conference Date : 10/10/2022 Subseries : Research talks arXiv category : Dynamical Systems ; Geometric Topology Mathematical Area(s) : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 00:59:46 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2022-10-10_Eynard_Bontemps.mp4 
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Information on the Event
Event Title : Big Mapping Class Groups and Diffeomorphism Groups / Gros groupes modulaires et groupes de difféomorphismesEvent Organizers : Mann, Kathryn ; Navas, Andrés ; Rivas, Cristóbal ; Triestino, Michele ; Valdez, Ferrán Dates : 10/10/2022 - 14/10/2022 Event Year : 2022 Event URL : https://conferences.cirm-math.fr/2612.html
Citation Data
DOI : 10.24350/CIRM.V.19968003Cite this video as: Eynard-Bontemps, Hélène (2022). Connectedness and deformation by conjugation of actions on [0,1] (or $^1). CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19968003 URI : http://dx.doi.org/10.24350/CIRM.V.19968003 |
See Also
- [Multi angle] Mapping class groups of infinite-type surfaces and their actions on hyperbolic graphs / Author of the conference Patel, Priyam.
- [Multi angle] On actions on the real line of some finitely generated groups / Author of the conference Matte Bon, Nicolás.
- [Multi angle] Irreducible lattices in semi-simple Lie groups of higher rank are not left-orderable / Author of the conference Hurtado Salazar, Sebastian.
- [Multi angle] Fine curve graphs and surface homeomorphisms / Author of the conference Hensel, Sebastian.
Bibliography
- 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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