Livsic theorem for diffeomorphism cocycles

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 second author and Potrie [KP16] to higher dimensions.

17 pages. Revised version after referee report. To appear in GAFA

References in corpus (2)

• The cohomological equation for partially hyperbolic diffeomorphisms
• Smooth dependence on parameters of solution of cohomology equations over Anosov systems and applications to cohomology equations on diffeomorphism groups

Cited by in corpus (5)

• The Burnside problem for ${\text{Diff}}_{\text{Vol}}({\mathbb{S}}^2)$
• Relating boundary and interior solutions of the cohomological equation for cocycles by isometries of negatively curved spaces. The Livsic case
• Diffeomorphism cocycles over partially hyperbolic systems
• Cohomology of fiber-bunched twisted cocycles over hyperbolic systems
• On the Integrability of codimension-one invariant subbundles of partially hyperbolic skew-products