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## Topological self-joinings of Cartan actions by toral automorphisms

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Pertenece a: Project Euclid (Hosted at Cornell University Library)

Descripción: 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.

Autor(es): Lindenstrauss, Elon -  Wang, Zhiren -

Id.: 55259221

Idioma: English  -

Versión: 1.0

Tipo:  application/pdf -

Palabras clave37C85 -

Tipo de recurso: Text  -

Audiencia: Estudiante  -  Profesor  -  Autor  -

Estructura: Atomic

Coste: no

: 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

Contacto:

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

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