Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.18757 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909407510528000 |
|---|---|
| author | Laureano, Rosário D. |
| author_facet | Laureano, Rosário D. |
| contents | After the fundamental work of Livschitz in [1; 2], various research directions emerged, among which the following stand out: (i) the study of cocycles with values in groups and semigroups beyond R, as well as the investigation of corresponding regularity results; (ii) the analysis of how a certain degree of regularity of the cocycle can confer corresponding regularity to the solution of the cohomological equation; and (iii) the study of higher-dimensional cohomology naturally associated with the action of groups other than Z or R. The aim of this article is to present, as self-contained as possible, a review of the natural generalizations of the notions of cocycles and cochains, as well as their corresponding results, in the study of cohomological equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18757 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cocycles in Lie Groups, Cochains and Regularity Problem Laureano, Rosário D. Dynamical Systems 22, 37 After the fundamental work of Livschitz in [1; 2], various research directions emerged, among which the following stand out: (i) the study of cocycles with values in groups and semigroups beyond R, as well as the investigation of corresponding regularity results; (ii) the analysis of how a certain degree of regularity of the cocycle can confer corresponding regularity to the solution of the cohomological equation; and (iii) the study of higher-dimensional cohomology naturally associated with the action of groups other than Z or R. The aim of this article is to present, as self-contained as possible, a review of the natural generalizations of the notions of cocycles and cochains, as well as their corresponding results, in the study of cohomological equations. |
| title | Cocycles in Lie Groups, Cochains and Regularity Problem |
| topic | Dynamical Systems 22, 37 |
| url | https://arxiv.org/abs/2411.18757 |