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Critical regularity and subexponential growth
Multi angle
Authors : Kim, Sang-Hyun (Author of the conference)
CIRM (Publisher )
20A15 - Applications of logic to group theory
57S05 - Topological properties of groups of homeomorphisms or diffeomorphisms
CIRM (Publisher )
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Abstract :
Two groups are elementarily equivalent if they have the same sets of true firstorder group theoretic sentences. We prove that if the homeomorphism groups of two compact connected manifolds are elementarily equivalent, then the manifolds are homeomorphic. This generalizes Whittaker's theorem on isomorphic homeomorphism groups (1963) without relying on it. Joint work with Thomas Koberda (UVa) and Javier de la Nuez-Gonzalez (KIAS).
Keywords : homeomorphism group; manifold, first order theory; elementary equivalence
MSC Codes : Keywords : homeomorphism group; manifold, first order theory; elementary equivalence
20A15 - Applications of logic to group theory
57S05 - Topological properties of groups of homeomorphisms or diffeomorphisms
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Information on the Video
Film maker : Recanzone, LucaLanguage : English Available date : 10/01/2025 Conference Date : 12/12/2024 Subseries : Research talks arXiv category : Group Theory ; Geometric Topology ; Logic Mathematical Area(s) : Geometry ; Logic and Foundations ; Topology Format : MP4 (.mp4) - HD Video Time : 01:04:02 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-12-12_Kim.mp4 
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Information on the Event
Event Title : Foliations and Diffeomorphism Groups / Feuilletages et Groupes de DifféomorphismeEvent Organizers : Eynard-Bontemps, Hélène ; Meigniez, Gaël ; Nariman, Sam ; Yazdi, Mehdi Dates : 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.20274803Cite this video as: Kim, Sang-Hyun (2024). Critical regularity and subexponential growth. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20274803 URI : http://dx.doi.org/10.24350/CIRM.V.20274803 |
See Also
- [Multi angle] On the group of real-analytic diffeomorphisms - lecture 3 / Author of the conference Takashi, Tsuboi.
- [Multi angle] On the group of real-analytic diffeomorphisms - lecture 2 / Author of the conference Takashi, Tsuboi.
- [Multi angle] On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 3 / Author of the conference Navas, Andrès.
- [Multi angle] On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 2 / Author of the conference Navas, Andrès.
- [Multi angle] Groups of Anosov-like homeomorphisms and foliations of the plane - lecture 3 / Author of the conference Mann, Kathryn.
- [Multi angle] Groups of Anosov-like homeomorphisms and foliations of the plane -Lecture 2 / Author of the conference Mann, Kathryn.
- [Multi angle] Veering triangulations and transverse foliations / Author of the conference Zung, Jonathan.
- [Multi angle] On the group of real-analytic diffeomorphisms - Lecture 1 / Author of the conference Takashi, Tsuboi.
- [Multi angle] Persistently foliar knots / Author of the conference Roberts, Rachel.
- [Multi angle] On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 1 / Author of the conference Navas, Andrès.
- [Multi angle] Using ergodic theory to study the cohomology of diffeomorphism groups / Author of the conference Monod, Nicolas.
- [Multi angle] Dynamics of surface homeomorphisms and fine curve graph / Author of the conference Militon, Emmanuel.
- [Multi angle] Taut foliations through a contact lens / Author of the conference Massoni, Thomas.
- [Multi angle] Groups of Anosov-like homeomorphisms and foliations of the plane - lecture 1 / Author of the conference Mann, Kathryn.
- [Multi angle] Torus homeomorphisms and the fine curve graph / Author of the conference Le Roux, Frédéric.
- [Multi angle] Recent progress on groups of area-preserving homeomorphisms / Author of the conference Humilière, Vincent.
- [Multi angle] Distortion elements in groups of interval diffeomorphisms / Author of the conference 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 $\mathbb{S}^{1}$ / Author of the conference Bonatti, Christian.
Bibliography
- KIM, Sang-hyun, KOBERDA, Thomas, et GONZÁLEZ, J. First order rigidity of homeomorphism groups of manifolds. arXiv preprint arXiv:2302.01481, 2023. - https://doi.org/10.48550/arXiv.2302.01481
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