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arXiv · 1401.1583

Quotient cohomology of certain 1- and 2-dimensional substitution tiling spaces

Enrico Paolo Bugarin·Franz Gähler
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Abstract

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.

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Enrico Paolo Bugarin, Franz Gähler. 2014-01-08. Quotient cohomology of certain 1- and 2-dimensional substitution tiling spaces. https://doi.org/10.12693/aphyspola.126.438

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