# Livšic theorem for diffeomorphism cocycles

Avila, Artur; Kocsard, Alejandro; Liu, Xiao-Chuan (2018). Livšic theorem for diffeomorphism cocycles. Geometric and Functional Analysis, 28(4):943-964.

## Abstract

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.

## Abstract

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.

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