Substitutions with Vanishing Rotationally Invariant First Cohomology

Juan García Escudero

Discrete Dynamics in Nature and Society, 2012, vol. 2012, 1-15

Abstract:

The cohomology groups of tiling spaces with three-fold and nine-fold symmetries are obtained. 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 ð ‘ if the underlying rotation group is ð ™ ð ‘ . When the symmetries are of crystallographic type, the cohomologies are infinitely generated.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:818549

DOI: 10.1155/2012/818549

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