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

页码：109 / 131

页数：23

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