Avila, Artur; Kocsard, Alejandro; Liu, Xiao-Chuan (2018). Livšic theorem for diffeomorphism cocycles. Geometric and Functional Analysis, 28(4):943-964.
We prove the so called Livšic theorem for cocycles taking values in the group of $C^{1+β}$ -diffeomorphisms of any closed manifold of arbitrary dimension. Since no localization hypothesis is assumed, this result is completely global in the space of cocycles and thus extends the previous result of the Kocsard and Potrie (Comment Math Helv 91:39–64, 2016) to higher dimensions.
We prove the so called Livšic theorem for cocycles taking values in the group of $C^{1+β}$ -diffeomorphisms of any closed manifold of arbitrary dimension. Since no localization hypothesis is assumed, this result is completely global in the space of cocycles and thus extends the previous result of the Kocsard and Potrie (Comment Math Helv 91:39–64, 2016) to higher dimensions.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Analysis
Physical Sciences > Geometry and Topology |
| Uncontrolled Keywords: | Geometry and Topology, Analysis |
| Language: | English |
| Date: | 1 July 2018 |
| Deposited On: | 15 Nov 2018 14:09 |
| Last Modified: | 29 Nov 2023 08:15 |
| Publisher: | Springer |
| ISSN: | 1016-443X |
| Additional Information: | This is a post-peer-review, pre-copyedit version of an article published in Geometric and Functinonal Analysis. The final authenticated version is available online at: https://doi.org/10.1007/s00039-018-0454-y |
| OA Status: | Green |
| Free access at: | Publisher DOI. An embargo period may apply. |
| Publisher DOI: | https://doi.org/10.1007/s00039-018-0454-y |
Avila, Artur