{
  "id": "1604.01246",
  "version": "v1",
  "published": "2016-04-05T13:12:40.000Z",
  "updated": "2016-04-05T13:12:40.000Z",
  "title": "Beyond primitivity for one-dimensional substitution tiling spaces",
  "authors": [
    "Gregory R. Maloney",
    "Dan Rust"
  ],
  "categories": [
    "math.DS",
    "math.AT"
  ],
  "abstract": "We study the topology and dynamics of subshifts and tiling spaces associated to non-primitive substitutions in one dimension. We identify a property of a substitution, which we call tameness, in the presence of which most of the possible pathological behaviours of non-minimal substitutions cannot occur. We prove that a strongly aperiodic substitution is tame, and use this to prove a slightly stronger version of a result of Durand, which says that the subshift of a minimal substitution is topologically conjugate to the subshift of a primitive substitution. We then extend to the non-minimal setting a result obtained by Anderson and Putnam for primitive substitutions, which says that a substitution tiling space is homeomorphic to an inverse limit of a certain CW complex under a self-map induced by the substitution. We use this result to explore the structure of the lattice of closed invariant subspaces and quotients of a substitution tiling space, for which we compute cohomological invariants that are stronger that the \\v{C}ech cohomology of the tiling space alone.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-05T13:12:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "55N05",
      "54H20",
      "37B50",
      "52C23"
    ],
    "keywords": [
      "one-dimensional substitution tiling spaces",
      "primitivity",
      "primitive substitution",
      "non-minimal substitutions",
      "slightly stronger version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160401246M"
    }
  }
}