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We show that if $r\geq3$ and $\alpha$ is a faithful $\mathbb {Z}^{r}$ -Cartan action on a torus $\mathbb {T}^{d}$ by automorphisms, then any closed subset of $(\mathbb {T}^{d})^{2}$ which is invariant and topologically transitive under the diagonal $\mathbb {Z}^{r}$ -action by $\alpha$ is homogeneous, in the sense that it is either the full torus $(\mathbb {T}^{d})^{2}$ , 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.

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Lindenstrauss, Elon -  Wang, Zhiren - 

Id.: 55259221

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras clave37C85 - 

Tipo de recurso: Text  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Copyright 2012 Duke University Press

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] 0012-7094
[References] 1547-7398

Fecha de contribución: 25-jul-2012


* Duke Math. J. 161, no. 7 (2012), 1305-1350
* doi:10.1215/00127094-1593290

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