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On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 2
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Authors : ... (Author of the conference)
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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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Abstract :
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
MSC Codes : 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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Information on the Video
Language : EnglishAvailable date : 10/01/2025 Conference Date : 10/12/2024 Subseries : Research School arXiv category : Dynamical Systems ; Functional Analysis ; Geometric Topology Mathematical Area(s) : Dynamical Systems & ODE ; Geometry ; Topology Format : MP4 (.mp4) - HD Video Time : 01:03:25 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-12-10_Navas_2.mp4 
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Information on the Event
Event Title : Foliations and Diffeomorphism Groups / Feuilletages et Groupes de DifféomorphismeDates : 09/12/2024 - 13/12/2024 Event Year : 2024 Event URL : https://conferences.cirm-math.fr/3082.html
Citation Data
DOI : 10.24350/CIRM.V.20276403Cite this video as: (2024). On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20276403 URI : http://dx.doi.org/10.24350/CIRM.V.20276403 |
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Bibliography
- 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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