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15 May 2012 Topological self-joinings of Cartan actions by toral automorphisms
Elon Lindenstrauss, Zhiren Wang
Duke Math. J. 161(7): 1305-1350 (15 May 2012). DOI: 10.1215/00127094-1593290

Abstract

We show that if r3 and α is a faithful Zr-Cartan action on a torus Td by automorphisms, then any closed subset of (Td)2 which is invariant and topologically transitive under the diagonal Zr-action by α is homogeneous, in the sense that it is either the full torus (Td)2, or a finite set of rational points, or a finite disjoint union of parallel translates of some d-dimensional invariant subtorus. A counterexample is constructed for the rank 2 case.

Citation

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Elon Lindenstrauss. Zhiren Wang. "Topological self-joinings of Cartan actions by toral automorphisms." Duke Math. J. 161 (7) 1305 - 1350, 15 May 2012. https://doi.org/10.1215/00127094-1593290

Information

Published: 15 May 2012
First available in Project Euclid: 4 May 2012

zbMATH: 1258.37031
MathSciNet: MR2922376
Digital Object Identifier: 10.1215/00127094-1593290

Subjects:
Primary: 37C85
Secondary: 37A45

Rights: Copyright © 2012 Duke University Press

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Vol.161 • No. 7 • 15 May 2012
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