Rigidity of higher rank abelian cocycles with values in diffeomorphism groups

A. Katok; V. Niţică

doi:10.1007/s10711-006-9116-6

Rigidity of higher rank abelian cocycles with values in diffeomorphism groups

A. Katok, V. Niţică

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

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)/Γ or SL(n,ℂ)/Γ, for n ≥ 3, and Γ torsion free cocompact lattice. The results in this paper rely on a technique developed recently by D. Damjanović and A. Katok.

Original language	English (US)
Pages (from-to)	109-131
Number of pages	23
Journal	Geometriae Dedicata
Volume	124
Issue number	1
DOIs	https://doi.org/10.1007/s10711-006-9116-6
State	Published - Feb 2007

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.1007/s10711-006-9116-6

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title = "Rigidity of higher rank abelian cocycles with values in diffeomorphism groups",

abstract = " 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)/Γ or SL(n,ℂ)/Γ, for n ≥ 3, and Γ torsion free cocompact lattice. The results in this paper rely on a technique developed recently by D. Damjanovi{\'c} and A. Katok.",

author = "A. Katok and V. Ni{\c t}ic{\u a}",

note = "Funding Information: Acknowledgments The research of AK was supported in part by NSF Grant DMS-0505539. The research of VN was supported in part by NSF Grant DMS-0500832. VN was supported by the Center for Dynamical Systems and Geometry at Penn State. This allowed him to visit Penn State during Fall 2006. We would like to thank D. Damjanovi{\'c} and D. Fisher for several comments about the paper.",

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T1 - Rigidity of higher rank abelian cocycles with values in diffeomorphism groups

AU - Katok, A.

AU - Niţică, V.

N1 - Funding Information: Acknowledgments The research of AK was supported in part by NSF Grant DMS-0505539. The research of VN was supported in part by NSF Grant DMS-0500832. VN was supported by the Center for Dynamical Systems and Geometry at Penn State. This allowed him to visit Penn State during Fall 2006. We would like to thank D. Damjanović and D. Fisher for several comments about the paper.

PY - 2007/2

Y1 - 2007/2

N2 - 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)/Γ or SL(n,ℂ)/Γ, for n ≥ 3, and Γ torsion free cocompact lattice. The results in this paper rely on a technique developed recently by D. Damjanović and A. Katok.

AB - 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)/Γ or SL(n,ℂ)/Γ, for n ≥ 3, and Γ torsion free cocompact lattice. The results in this paper rely on a technique developed recently by D. Damjanović and A. Katok.

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Rigidity of higher rank abelian cocycles with values in diffeomorphism groups

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