{
  "id": "math/0010222",
  "version": "v1",
  "published": "2000-10-24T05:06:47.000Z",
  "updated": "2000-10-24T05:06:47.000Z",
  "title": "Spaces of embeddings of compact polyhedra into 2-manifolds",
  "authors": [
    "Tatsuhiko Yagasaki"
  ],
  "comment": "13 pages",
  "categories": [
    "math.GT",
    "math.GN"
  ],
  "abstract": "Let M be a PL 2-manifold and X be a compact subpolyhedron of M and let E(X, M) denote the space of embeddings of X into M with the compact-open topology. In this paper we study an extension property of embeddings of X into M and show that the restriction map from the homeomorphism group of M to E(X, M) is a principal bundle. As an application we show that if M is a Euclidean PL 2-manifold and dim X >= 1 then the triple (E(X,M), E^LIP(X,M), E^PL(X, M)) is an (s,Sigma,sigma)-manifold, where E_K^LIP(X,M) and E_K^PL(X, M) denote the subspaces of Lipschitz and PL embeddings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-10-24T05:06:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N05",
      "57N20",
      "57N35"
    ],
    "keywords": [
      "compact polyhedra",
      "pl embeddings",
      "euclidean pl",
      "compact-open topology",
      "principal bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.....10222Y"
    }
  }
}