{
  "id": "2008.01643",
  "version": "v1",
  "published": "2020-08-04T15:37:21.000Z",
  "updated": "2020-08-04T15:37:21.000Z",
  "title": "Decoupling decorations on moduli spaces of manifolds",
  "authors": [
    "Luciana Basualdo Bonatto"
  ],
  "comment": "32 pages, 2 figures. Comments welcome!",
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "We consider moduli spaces of $d$-dimensional manifolds with embedded particles and discs. In this moduli space, the location of the particles and discs is constrained by the $d$-dimensional manifold. We will compare this moduli space with the moduli space of $d$-dimensional manifolds in which the location of such decorations is no longer constrained, i.e. the decorations are decoupled. We generalise work by B\\\"odigheimer--Tillmann for oriented surfaces and obtain new results for surfaces with different tangential structures as well as to higher dimensional manifolds. We also provide a generalisation of this result to moduli spaces with more general submanifold decorations and specialise in the case of decorations being unparametrised unlinked circles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-04T15:37:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R40",
      "57R15",
      "57R50",
      "57S05",
      "55R80"
    ],
    "keywords": [
      "moduli space",
      "decoupling decorations",
      "general submanifold decorations",
      "higher dimensional manifolds",
      "generalise work"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}