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Local rigidity for certain groups of toral automorphisms

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Abstract

Let Γ = SL(n, ℤ) or any subgroup of finite index, n ≥ 4. We show that the standard action of Γ on\(\mathbb{T}\) n is locally rigid, i.e., every action of Γ on\(\mathbb{T}\) n by C∞ diffeomorphisms which is sufficiently close to the standard action is conjugate to the standard action by a C∞ diffeomorphism. In the course of the proof, we obtain a global rigidity result (Theorem 4.12) for actions of free abelian subgroups of maximal rank in SL(n, ℤ).

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Authors and Affiliations

  1. Department of Mathematics, Pennsylvania State University, 16803, University Park, PA, USA

    A. Katok

  2. Mathematical Sciences Research Institute, 1000 Centennial Drive, 94720, Berkeley, CA, USA

    J. Lewis

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  1. A. Katok
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  2. J. Lewis
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Partially supported by NSF grant DMS9011749.

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Katok, A., Lewis, J. Local rigidity for certain groups of toral automorphisms. Israel J. Math. 75, 203–241 (1991). https://doi.org/10.1007/BF02776025

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  • DOI: https://doi.org/10.1007/BF02776025

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