Cohomology in one-dimensional substitution tiling spaces

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dc.creatorBarge, Marcy
dc.creatorDiamond, Beverly
dc.date2007-02-22
dc.date.accessioned2026-07-07T07:48:14Z
dc.date.available2026-07-07T07:48:14Z
dc.descriptionAnderson 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.
dc.identifierhttps://arxiv.org/abs/math/0702669
dc.identifierhttp://arxiv.org/abs/math/0702669
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124426
dc.subjectDynamical Systems
dc.subjectGeneral Topology
dc.subject37B05; 55N05; 54H20
dc.titleCohomology in one-dimensional substitution tiling spaces
dc.typetext

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