{
  "id": "1705.03836",
  "version": "v1",
  "published": "2017-05-10T16:02:04.000Z",
  "updated": "2017-05-10T16:02:04.000Z",
  "title": "Sum of embedded submanifolds",
  "authors": [
    "Csaba Nagy"
  ],
  "comment": "26 pages, 4 figures. Submitted to Homology, Homotopy and Applications",
  "categories": [
    "math.GT"
  ],
  "abstract": "In an $n$-manifold $X$ each element of $H_{n-1}(X; \\mathbb{Z}_2)$ can be represented by an embedded codimension-1 submanifold. Hence for any two such submanifolds there is a third one that represents the sum of their homology classes. We construct such a representative explicitly. We describe the analogous construction for codimension-2 co-oriented submanifolds, and examine the special case of oriented and/or co-oriented submanifolds. We also give a lower bound for the number of connected components of the intersection of two oriented codimension-1 submanifolds in terms of the homology classes they represent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-10T16:02:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R40",
      "57R95"
    ],
    "keywords": [
      "embedded submanifolds",
      "homology classes",
      "co-oriented submanifolds",
      "special case",
      "lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}