Global rigidity results for lattice actions on tori and new examples of volume-preserving actions |
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Authors: | A. Katok J. Lewis |
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Affiliation: | (1) Department of Mathematics, Pennsylvania State University, 16802 University Park, PA, USA;(2) Renaissance Software, Inc., 175 S. San Antonio Road, 94022 Los Altos, CA, USA |
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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. This work was partially supported by NSF grant DMS9017995. |
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