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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Transversely Cantor laminations as inverse limits


Authors: Fernando Alcalde Cuesta, Álvaro Lozano Rojo and Marta Macho Stadler
Journal: Proc. Amer. Math. Soc. 139 (2011), 2615-2630
MSC (2010): Primary 57R05, 57R30
Published electronically: December 8, 2010
MathSciNet review: 2784831
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Abstract: We demonstrate that any minimal transversely Cantor compact lamination of dimension $ p$ and class $ C^1$ without holonomy is an inverse limit of compact branched manifolds of dimension $ p$. To prove this result, we extend the triangulation theorem for $ C^1$ manifolds to transversely Cantor $ C^1$ laminations. In fact, we give a simple proof of this classical theorem based on the existence of $ C^1$-compatible differentiable structures of class $ C^\infty$.


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Additional Information

Fernando Alcalde Cuesta
Affiliation: Department of Geometry and Topology, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
Email: fernando.alcalde@usc.es

Álvaro Lozano Rojo
Affiliation: Department of Mathematics, University of the Basque Country, 48940 Leioa, Spain
Email: alvaro.lozano@ehu.es

Marta Macho Stadler
Affiliation: Department of Mathematics, University of the Basque Country, 48940 Leioa, Spain
Email: marta.macho@ehu.es

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10665-2
PII: S 0002-9939(2010)10665-2
Keywords: Lamination, triangulation, branched manifold, inverse limit.
Received by editor(s): February 25, 2010
Received by editor(s) in revised form: June 25, 2010
Published electronically: December 8, 2010
Additional Notes: This work was partially supported by MEC MTM2007-66262, UPV 00127.310-E-14790, EHU 06/05 and Xunta de Galicia INCITE07PXIE1R207053ES
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.