Affability of Euclidean tilings

Fernando Alcalde Cuesta; Pablo González Sequeiros; Álvaro Lozano Rojo

doi:10.1016/j.crma.2009.06.011

Dynamical Systems

Affability of Euclidean tilings

Presented by: Étienne Ghys

Fernando Alcalde Cuesta ¹; Pablo González Sequeiros ¹; Álvaro Lozano Rojo ²

¹ Dpto. Xeometría e Topoloxía, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
² Dpto. Matemáticas, Universidad del País Vasco-Euskal Herriko Unibertsitatea, 48940 Leioa, Spain

Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 947-952.

Abstract
Résumé

We prove that every minimal equivalence relation on a Cantor set arising from the continuous hull of an aperiodic and repetitive Euclidean tiling is affable.

Nous prouvons que toute relation d'équivalence définie sur l'ensemble de Cantor par l'enveloppe d'un pavage euclidien apériodique et répétitif est affable.

Received: 2007-12-11
Accepted: 2009-06-17
Published online: 2009-07-02

DOI: 10.1016/j.crma.2009.06.011

Author's affiliations:

Fernando Alcalde Cuesta ¹; Pablo González Sequeiros ¹; Álvaro Lozano Rojo ²

¹ Dpto. Xeometría e Topoloxía, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
² Dpto. Matemáticas, Universidad del País Vasco-Euskal Herriko Unibertsitatea, 48940 Leioa, Spain

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     title = {Affability of {Euclidean} tilings},
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Fernando Alcalde Cuesta; Pablo González Sequeiros; Álvaro Lozano Rojo. Affability of Euclidean tilings. Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 947-952. doi : 10.1016/j.crma.2009.06.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.06.011/

References
Cited by

[1] F. Alcalde Cuesta; Á. Lozano Rojo; M. Macho Stadler Dynamique transverse de la lamination de Ghys–Kenyon, Astérisque, Volume 323 (2009)

[2] J. Bellissard; R. Benedetti; J.M. Gambaudo Spaces of tilings, finite telescopic approximations and gap-labelling, Comm. Math. Phys., Volume 261 (2006), pp. 1-41

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[7] T. Giordano; H. Matui; I. Putnam; C. Skau Orbit equivalence for Cantor minimal $Z^{d}$ -systems | arXiv

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[9] Á. Lozano Rojo, Dinámica transversa de laminaciones definidas por grafos repetitivos, UPV-EHU Ph.D. thesis, 2008

[10] H. Matui Affability of equivalence relations arising from two-dimensional substitution tilings, Ergodic Theory Dynam. Systems, Volume 26 (2006), pp. 467-480

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[12] S. Petite On invariant measures of finite affine type tilings, Ergodic Theory Dynam. Systems, Volume 26 (2006), pp. 1159-1176

[13] R.M. Robinson Undecidability and nonperiodicity of tilings of the plane, Invent. Math., Volume 12 (1971), pp. 177-209

[14] C. Series Foliations of polynomial growth are hyperfinite, Israel J. Math., Volume 34 (1979), pp. 245-258

Cited by Sources:

^☆ This work was supported by the Spanish Ministry of Education and Science (Research Projects MTM2004-08214 and MTM2007-66262), the University of the Basque Country (R. Project EHU 06/05), and the Spanish Network of Topology.

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