Quotient Cohomology of Certain 1- and 2-Dimensional Substitution Tiling Spaces

E.P. Bugarin and F. Gähler Fakultät für Mathematik, Universität Bielefeld, Universitätsstraße 25, D-33615 Bielefeld, Germany

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The quotient cohomology of tiling spaces is a topological invariant that relates a tiling space to one of its factors, viewed as topological dynamical systems. In particular, it is a relative version: of the tiling cohomology that distinguishes factors of tiling spaces. In this work, the quotient cohomologies within certain families of substitution tiling spaces in 1 and 2 dimensions are determined. Specifically, the quotient cohomologies for the family of the generalised Thue-Morse sequences and generalised chair tilings are presented.

DOI: 10.12693/APhysPolA.126.438 PACS numbers: 02.40.Re, 45.30.+s