English
On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 3
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).
Mots-Clés : centralizer; flow; conjugate actions
Codes MSC : Mots-Clés : 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 : Recanzone, LucaLangue : Anglais Date de Publication : 10/01/2025 Date de Captation : 11/12/2024 Sous Collection : Research School Catégorie arXiv : Dynamical Systems ; Functional Analysis ; Geometric Topology Domaine(s) : Systèmes Dynamiques & EDO ; Géométrie ; Topologie Format : MP4 (.mp4) - HD Durée : 01:00:23 Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-12-11_Navas_3.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 de la Rencontre : https://conferences.cirm-math.fr/3082.html
Données de citation
DOI : 10.24350/CIRM.V.20276503Citer cette vidéo: Navas, Andrès (2024). On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 3. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20276503 URI : http://dx.doi.org/10.24350/CIRM.V.20276503 |
Voir Aussi
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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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