2007/02/22 by Marcy Barge, Barge, Marcy, Beverly Diamond +1
Materials Science · Mathematics · #37B05 #54H20 #55N05 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN) #Quasicrystal Structures and Properties #math.DS #math.GN #msc:37B05 #msc:54H20 #msc:55N05
paper · pdf · doi:10.48550/arxiv.math/0702669
arxiv created 2007/02/22 · openalex publication_date 2007/02/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 modification 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.