{
  "id": "math/0402119",
  "version": "v1",
  "published": "2004-02-08T01:57:09.000Z",
  "updated": "2004-02-08T01:57:09.000Z",
  "title": "Non-zero degree maps between $2n$-manifolds",
  "authors": [
    "Haibao Duan",
    "Shicheng Wang"
  ],
  "comment": "18 pages",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "Thom-Pontrjagin constructions are used to give a computable necessary and sufficient condition when a homomorphism $\\phi : H^n(L;Z)\\to H^n(M;Z)$ can be realized by a map $f:M\\to L$ of degree $k$ for closed $(n-1)$-connected $2n$-manifolds $M$ and $L$, $n>1$. A corollary is that each $(n-1)$-connected $2n$-manifold admits selfmaps of degree larger than 1, $n>1$. In the most interesting case of dimension 4, with the additional surgery arguments we give a necessary and sufficient condition for the existence of a degree $k$ map from a closed orientable 4-manifold $M$ to a closed simply connected 4-manifold $L$ in terms of their intersection forms, in particular there is a map $f:M\\to L$ of degree 1 if and only if the intersection form of $L$ is isomorphic to a direct summand of that of $M$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-02-08T01:57:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R19",
      "55M25"
    ],
    "keywords": [
      "non-zero degree maps",
      "intersection form",
      "sufficient condition",
      "additional surgery arguments",
      "manifold admits selfmaps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......2119D"
    }
  }
}