{
  "id": "2206.06329",
  "version": "v1",
  "published": "2022-06-13T17:26:27.000Z",
  "updated": "2022-06-13T17:26:27.000Z",
  "title": "Topological Bordism of Singular Spaces and an Application to Stratified L-Classes",
  "authors": [
    "Martin Rabel"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly, instead of restricting geometric cycles by conditions on links only, a more flexible framework is built directly via geometric properties, secondly, controlled topology methods are used to give an accessible link-based criterion to detect suitable cycles and thirdly, a geometric argument is used to show, that these classes of cycles are suitable to study the transition to intrinsic stratifications. As an application, we give a construction of topologically (homeomorphism) invariant (homological) L-classes on MHSS Witt-spaces satisfying conditions on Whitehead-groups of links and the dimensional spacing of meeting strata. These L-classes agree, whenever those spaces are additionally pl-pseudomanifolds, with the Goresky-MacPherson L-classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-13T17:26:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N20",
      "55N22",
      "55N33",
      "57N75",
      "57N80",
      "57R20"
    ],
    "keywords": [
      "singular spaces",
      "stratified l-classes",
      "topological bordism",
      "application",
      "manifold homotopy stratified sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}