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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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Additional indexing

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 Jul 2020 07:58
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

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