Using ergodic theory to study the cohomology of diffeomorphism groups | Vidéo | Carmin.tv

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Using ergodic theory to study the cohomology of diffeomorphism groups

By Nicolas Monod

Appears in collection : Foliations and Diffeomorphism Groups / Feuilletages et Groupes de Difféomorphisme

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.

Information about the video

Date of recording 12/12/2024
Date of publication 10/01/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20275403
Cite this video Monod, Nicolas (12/12/2024). Using ergodic theory to study the cohomology of diffeomorphism groups. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20275403
URL https://dx.doi.org/10.24350/CIRM.V.20275403

Domain(s)

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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