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Rigidity of higher rank abelian cocycles with values in diffeomorphism groups

被引：6
|
作者：
Katok, A. [1 ]
Nitica, V.
机构：
[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA
[2] W Chester Univ, Dept Math, W Chester, PA 19383 USA
[3] Acad Romana, Inst Math, Bucharest 70700, Romania
来源：
GEOMETRIAE DEDICATA | 2007年 / 124卷 / 01期
关键词：
rigidity; cocycle; cohomological equation; higher-rank abelian actions; diffeomorphism groups; partially hyperbolic diffeomorphism; Cartan actions;
D O I：
10.1007/s10711-006-9116-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider cocycles over certain hyperbolic R-k actions, k >= 2, and show rigidity properties for cocycles with values in a Lie group or a diffeomorphism group, which are close to identity on a set of generators, and are sufficiently smooth. The actions we consider are Cartan actions of SL(n, R)/ Gamma or SL(n, C)/ Gamma, for n >= 3, and Gamma torsion free cocompact lattice. The results in this paper rely on a technique developed recently by D. Damjanovic and A. Katok.
引用
收藏
页码：109 / 131
页数：23
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