| 1 LOCAL RIGIDITY OF PARTIALLY HYPERBOLIC ACTIONS. II. THE GEOMETRIC METHOD AND RESTRICTIONS OF WEYL CHAMBER FLOWS ON (2009) | |||||||||||||||
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| Abstract. We consider the restriction α0,G of the Weyl chamber flow on SL(n, R)/Γ (where Γ is a cocompact lattice) to a closed subgroup G isomorphic to Z k × R l, k + l ≥ 2 of the group D+ of positive diagonal matrices which contains a lattice in a twodimensional plane in general position. We prove that any C 2 small smooth perturbation of the action α0,G is differentiably conjugate to a standard perturbation which arises from a perturbation of the embedding Z k × R l → D+. We introduce a new method in rigidity of actions of higher rank abelian groups based on the study of combinatorial structure of the the web of Lyapunov (unipotent) foliations. Insights from the classical algebraic K-theory play a crucial role in establishing stability properties of that web. The method has applications to other classes of partially hyperbolic algebraic actions and is complementary to the other new analytic method which we introduced in the first paper of this series. 1. | |||||||||||||||
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