Researchers from University of Oviedo Report on Findings in Discrete and Continuous Dynamical Systems
2012 APR 10 - (VerticalNews.com) -- "The cohomology groups of tiling spaces with three-fold and nine-fold symmetries are obtained," scientists in Oviedo, Spain report.
"The substitution tilings are characterized by the fact that they have vanishing first cohomology group in the space of tilings modulo a rotation. The rank of the rational first cohomology, in the tiling space formed by the closure of a translational orbit, equals the Euler totient function evaluated at N if the underlying rotation group is Z(N)," wrote J.G. Escudero and colleagues, University of Oviedo.
The researchers concluded: "When the symmetries are of crystallographic type, the cohomologies are infinitely generated."
Escudero and colleagues published their study in Discrete Dynamics in Nature and Society (Substitutions with Vanishing Rotationally Invariant First Cohomology. Discrete Dynamics in Nature and Society, 2012;():1-15).
For additional information, contact J.G. Escudero, University of Oviedo, Fac Ciencias Matemat & Fis, Oviedo 33007, Spain.
The publisher's contact information for the journal Discrete Dynamics in Nature and Society is: Hindawi Publishing Corporation, 410 Park Avenue, 15TH Floor, #287 Pmb, New York, NY 10022, USA.
Keywords: City:Oviedo, Country:Spain, Region:Europe, Discrete and Continuous Dynamical Systems
This article was prepared by VerticalNews Mathematics editors from staff and other reports. Copyright 2012, VerticalNews Mathematics via VerticalNews.com.