English
On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 1
Multi angle
Auteurs : Navas, Andrès (Auteur de la Conférence)
CIRM (Editeur )
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 (Editeur )
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Résumé :
Studying the (closure of the) (semi-)conjugacy class of a given group action on a 1-manifold is interesting from many points of view. Depending on the manifold and/or the differentiability involved, one is faced with problems concerning small denominators, growth of groups / orbits, distortion elements, bounded cohomology, group orderability, etc. In this minicourse we will explore several general results on this topic such as the $C^1$ smoothing via (semi-)conjugacies of small group actions and obstructions in class $C^2$ and higher. We will also explore some of the ideas involved in the proof of the connectedness of the space of $\mathbb{Z}^d$ actions by diffeomorphisms of $C^{1+ac}$ regularity (obtained in collaboration with H. Eynard-Bontemps).
Keywords : centralizer; flow; conjugate actions
Codes MSC : Keywords : centralizer; flow; conjugate 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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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 10/01/2025 Date de captation : 09/12/2024 Sous collection : Research School arXiv category : Dynamical Systems ; Functional Analysis ; Geometric Topology Domaine : Dynamical Systems & ODE ; Geometry ; Topology Format : MP4 (.mp4) - HD Durée : 01:00:57 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2021-12-09_Navas_1.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Foliations and Diffeomorphism Groups / Feuilletages et Groupes de DifféomorphismeOrganisateurs de la rencontre : Eynard-Bontemps, Hélène ; Meigniez, Gaël ; Nariman, Sam ; Yazdi, Mehdi Dates : 09/12/2024 - 13/12/2024 Année de la rencontre : 2024 URL Congrès : https://conferences.cirm-math.fr/3082.html
Données de citation
DOI : 10.24350/CIRM.V.20275503Citer cette vidéo: Navas, Andrès (2024). On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 1 . CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20275503 URI : http://dx.doi.org/10.24350/CIRM.V.20275503 |
Voir aussi
- [Multi angle] On the group of real-analytic diffeomorphisms - lecture 3 / Auteur de la Conférence Takashi, Tsuboi.
- [Multi angle] On the group of real-analytic diffeomorphisms - lecture 2 / Auteur de la Conférence Takashi, Tsuboi.
- [Multi angle] On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 3 / Auteur de la Conférence Navas, Andrès.
- [Multi angle] On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 2 / Auteur de la Conférence Navas, Andrès.
- [Multi angle] Groups of Anosov-like homeomorphisms and foliations of the plane - lecture 3 / Auteur de la Conférence Mann, Kathryn.
- [Multi angle] Groups of Anosov-like homeomorphisms and foliations of the plane -Lecture 2 / Auteur de la Conférence Mann, Kathryn.
- [Multi angle] Veering triangulations and transverse foliations / Auteur de la Conférence Zung, Jonathan.
- [Multi angle] On the group of real-analytic diffeomorphisms - Lecture 1 / Auteur de la Conférence Takashi, Tsuboi.
- [Multi angle] Persistently foliar knots / Auteur de la Conférence Roberts, Rachel.
- [Multi angle] Using ergodic theory to study the cohomology of diffeomorphism groups / Auteur de la Conférence Monod, Nicolas.
- [Multi angle] Dynamics of surface homeomorphisms and fine curve graph / Auteur de la Conférence Militon, Emmanuel.
- [Multi angle] Taut foliations through a contact lens / Auteur de la Conférence Massoni, Thomas.
- [Multi angle] Groups of Anosov-like homeomorphisms and foliations of the plane - lecture 1 / Auteur de la Conférence Mann, Kathryn.
- [Multi angle] Torus homeomorphisms and the fine curve graph / Auteur de la Conférence Le Roux, Frédéric.
- [Multi angle] Critical regularity and subexponential growth / Auteur de la Conférence Kim, Sang-Hyun.
- [Multi angle] Recent progress on groups of area-preserving homeomorphisms / Auteur de la Conférence Humilière, Vincent.
- [Multi angle] Distortion elements in groups of interval diffeomorphisms / Auteur de la Conférence Eynard-Bontemps, Hélène.
- [Multi angle] Foliations on the plane $ \mathbb{R}^{2}$, pre-laminations on the circle $\mathbb{S}^{1}$, group actions on the circle $\mathbb{S}^{1}$ / Auteur de la Conférence Bonatti, Christian.
Bibliographie
- EYNARD-BONTEMPS, Hélène et NAVAS, Andrés. The space of $ C^{1+ ac} $ actions of $\mathbb {Z}^ d $ on a one-dimensional manifold is path-connected. arXiv preprint arXiv:2306.17731, 2023. - https://doi.org/10.48550/arXiv.2306.17731
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