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arXiv · 1112.1475

Cohomology of One-dimensional Mixed Substitution Tiling Spaces

Franz Gähler·Gregory R. Maloney
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Abstract

We compute the Cech cohomology with integer coefficients of one-dimensional tiling spaces arising from not just one, but several different substitutions, all acting on the same set of tiles. These calculations involve the introduction of a universal version of the Anderson-Putnam complex. We show that, under a certain condition on the substitutions, the projective limit of this universal Anderson-Putnam complex is isomorphic to the tiling space, and we introduce a simplified universal Anderson-Putnam complex that can be used to compute Cech cohomology. We then use this simplified complex to place bounds on the rank of the first cohomology group of a one-dimensional substitution tiling space in terms of the number of tiles.

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Franz Gähler, Gregory R. Maloney. 2012-03-06. Cohomology of One-dimensional Mixed Substitution Tiling Spaces. https://arxiv.org/abs/1112.1475

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