Cocycles in Lie Groups, Cochains and Regularity Problem

Rosário D. Laureano

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arXiv · 2411.18757

Cocycles in Lie Groups, Cochains and Regularity Problem

Rosário D. Laureano

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Abstract

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.

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Rosário D. Laureano. 2024-11-27. Cocycles in Lie Groups, Cochains and Regularity Problem. https://arxiv.org/abs/2411.18757

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