Rigidity of higher rank abelian cocycles with values in diffeomorphism groups期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Rigidity of higher rank abelian cocycles with values in diffeomorphism groups

Authors:	A Katok V Ni?ic?

Institution:	(1) Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA;(2) Department of Mathematics, West Chester University, 323 Anderson Hall, West Chester, PA 19383, USA;(3) Institute of Mathematics of the Romanian Academy, P.O. Box 1–764, Bucharest, 70700, Romania

Abstract:	We consider cocycles over certain hyperbolic ${\mathbb{R}^k}$ actions, ${k\ge 2}$ , 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 ${SL(n,\mathbb{R})/\Gamma}$ or ${SL(n,\mathbb{C})/\Gamma}$ , for ${n\ge 3}$ , and Γ torsion free cocompact lattice. The results in this paper rely on a technique developed recently by D. Damjanović and A. Katok.

Keywords:	Rigidity Cocycle Cohomological equation Higher-rank abelian actions Diffeomorphism groups Partially hyperbolic diffeomorphism Cartan actions
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