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Global rigidity results for lattice actions on tori and new examples of volume-preserving actions

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Abstract

Any action of a finite index subgroup in SL(n,ℤ),n≥4 on then-dimensional torus which has a finite orbit and contains an Anosov element which splits as a direct product is smoothly conjugate to an affine action. We also construct first examples of real-analytic volume-preserving actions of SL(n,ℤ) and other higher-rank lattices on compact manifolds which are not conjugate (even topologically) to algebraic models.

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Authors and Affiliations

  1. Department of Mathematics, Pennsylvania State University, 16802, University Park, PA, USA

    A. Katok

  2. Renaissance Software, Inc., 175 S. San Antonio Road, 94022, Los Altos, CA, USA

    J. Lewis

Authors
  1. A. Katok
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  2. J. Lewis
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Correspondence to A. Katok.

Additional information

This work was partially supported by NSF grant DMS9017995.

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Katok, A., Lewis, J. Global rigidity results for lattice actions on tori and new examples of volume-preserving actions. Israel J. Math. 93, 253–280 (1996). https://doi.org/10.1007/BF02761106

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  • DOI: https://doi.org/10.1007/BF02761106

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