anosov actions
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2020 ◽  
Vol 238 (2) ◽  
pp. 745-806
Author(s):  
Danijela Damjanović ◽  
Disheng Xu

2018 ◽  
Vol 40 (1) ◽  
pp. 117-141 ◽  
Author(s):  
DANIJELA DAMJANOVIĆ ◽  
DISHENG XU

We prove that every smooth diffeomorphism group valued cocycle over certain$\mathbb{Z}^{k}$Anosov actions on tori (and more generally on infranilmanifolds) is a smooth coboundary on a finite cover, if the cocycle is center bunched and trivial at a fixed point. For smooth cocycles which are not trivial at a fixed point, we have smooth reduction of cocycles to constant ones, when lifted to the universal cover. These results on cocycle trivialization apply, via the existing global rigidity results, to maximal Cartan$\mathbb{Z}^{k}$($k\geq 3$) actions by Anosov diffeomorphisms (with at least one transitive), on any compact smooth manifold. This is the first rigidity result for cocycles over$\mathbb{Z}^{k}$actions with values in diffeomorphism groups which does not require any restrictions on the smallness of the cocycle or on the diffeomorphism group.


2017 ◽  
Vol 287 (3-4) ◽  
pp. 1279-1305
Author(s):  
Thierry Barbot ◽  
Carlos Maquera
Keyword(s):  

2013 ◽  
Vol 160 (1) ◽  
pp. 199-219 ◽  
Author(s):  
Thierry Barbot ◽  
Carlos Maquera

2012 ◽  
Vol 26 (1) ◽  
pp. 167-198 ◽  
Author(s):  
David Fisher ◽  
Boris Kalinin ◽  
Ralf Spatzier

2011 ◽  
Vol 15 (1) ◽  
pp. 191-216 ◽  
Author(s):  
David Fisher ◽  
Boris Kalinin ◽  
Ralf Spatzier
Keyword(s):  

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