Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 136, Issue 6, Pages 2183-2191Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0002-9939-08-09225-3
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Anderson and Putnam showed that the cohomology of a substitution tiling space may be computed by collaring tiles to obtain a substitution which forces its border. One can then represent the tiling space as an inverse limit of an inflation and substitution map on a cellular complex formed from the collared tiles; the cohomology of the tiling space is computed as the direct limit of the homomorphism induced by inflation and substitution on the cohomology of the complex. For one-dimensional substitution tiling spaces, we describe a modi. cation of the Anderson-Putnam complex on collared tiles that allows for easier computation and provides a means of identifying certain special features of the tiling space with particular elements of the cohomology.
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