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Using ergodic theory to study the cohomology of diffeomorphism groups
Multi angle
Authors : Monod, Nicolas (Author of the conference)
CIRM (Publisher )
CIRM (Publisher )
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Abstract :
Recent work with Nariman and with Fournier-Facio-Nariman determines the bounded cohomology of some familiar diffeomorphism groups. The results differ from what is known or expected in ordinary cohomology. Another way to phrase this is that certain classical characteristic classes are unbounded. The goal of this lecture is to show how some ideas from ergodic theory are useful to prove such cohomological results.
MSC Codes : |
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 ; Algebraic Topology ; Geometric Topology Mathematical Area(s) : Algebra ; Dynamical Systems & ODE ; Topology Format : MP4 (.mp4) - HD Video Time : 01:01:02 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-12-12_Monod.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.20275403Cite this video as: Monod, Nicolas (2024). Using ergodic theory to study the cohomology of diffeomorphism groups. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20275403 URI : http://dx.doi.org/10.24350/CIRM.V.20275403 |
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] 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] Critical regularity and subexponential growth / Author of the conference Kim, Sang-Hyun.
- [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
- MONOD, Nicolas. Lamplighters and the bounded cohomology of Thompson's group. Geometric and Functional Analysis, 2022, vol. 32, no 3, p. 662-675. - https://doi.org/10.1007/s00039-022-00604-9
- MONOD, Nicolas et NARIMAN, Sam. Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups. Inventiones mathematicae, 2023, vol. 232, no 3, p. 1439-1475. - https://doi.org/10.1007/s00222-023-01181-w
- FOURNIER-FACIO, Francesco, MONOD, Nicolas, NARIMAN, Sam, et al. The bounded cohomology of transformation groups of Euclidean spaces and discs. arXiv preprint arXiv:2405.20395, 2024. - https://doi.org/10.48550/arXiv.2405.20395
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