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Differentiable rigidity for hyperbolic toral actions

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Abstract

Our aim is to extend existing results about differentiable rigidity of higher rank abelian actions by automorphisms of a torus. Previous proofs have required an assumption of semisimplicity, that is, that the action is by commuting diagonalizable matrices. Here we introduce a technique that utilizes the unipotent part of a non-semisimple action, which allows us to discard the semisimplicity assumption. In its place we will make a technical assumption that the spectrum of the action restricted to leaves of the coarse Lyapunov decomposition is sufficiently narrow.

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ, 08544-1000, USA

    Manfred Einsiedler

  2. Department of Mathematics, Pennsylvania State University, McAllister Building, University Park, PA, 16802, USA

    Travis Fisher

Authors
  1. Manfred Einsiedler
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  2. Travis Fisher
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Einsiedler, M., Fisher, T. Differentiable rigidity for hyperbolic toral actions. Isr. J. Math. 157, 347–377 (2007). https://doi.org/10.1007/s11856-006-0016-0

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  • DOI: https://doi.org/10.1007/s11856-006-0016-0

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