Substitutions with Vanishing Rotationally Invariant First Cohomology | Zendy

Juan Garcı́a Escudero | Zendy

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Substitutions with Vanishing Rotationally Invariant First Cohomology

Author(s) -

Juan Garcı́a Escudero

Publication year - 2012

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2012/818549

Subject(s) - homogeneous space , mathematics , combinatorics , equivariant cohomology , invariant (physics) , font , cohomology , matrix (chemical analysis) , group cohomology , quotient , scalable vector graphics , group (periodic table) , pure mathematics , physics , geometry , mathematical physics , computer science , quantum mechanics , materials science , composite material , operating system

The cohomology groups of tiling spaces with three-fold and nine-fold symmetriesare obtained. The substitution tilings are characterized by the fact that they have vanishingfirst cohomology group in the space of tilings modulo a rotation. The rank of the rational firstcohomology, in the tiling space formed by the closure of a translational orbit, equals the Eulertotient function evaluated at if the underlying rotation group is . When the symmetriesare of crystallographic type, the cohomologies are infinitely generated

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