{
  "id": "2005.02744",
  "version": "v1",
  "published": "2020-05-06T11:29:36.000Z",
  "updated": "2020-05-06T11:29:36.000Z",
  "title": "Positive scalar curvature on spin pseudomanifolds: the fundamental group and secondary invariants",
  "authors": [
    "Boris Botvinnik",
    "Paolo Piazza",
    "Jonathan Rosenberg"
  ],
  "comment": "36 pages",
  "categories": [
    "math.DG",
    "math.KT"
  ],
  "abstract": "In this paper we continue the study of positive scalar curvature (psc) metrics on a depth-1 Thom-Mather stratified space $M_\\Sigma$ with singular stratum $\\beta M$ (a closed manifold of positive codimension) and associated link equal to $L$, a smooth compact manifold. We briefly call such spaces manifolds with $L$-fibered singularities. Under suitable spin assumptions we give necessary index-theoretic conditions for the existence of wedge metrics of positive scalar curvature. Assuming in addition that $L$ is a simply connected homogeneous space of positive scalar curvature, $L=G/H$, with the semisimple compact Lie group $G$ acting transitively on $L$ by isometries, we investigate when these necessary conditions are also sufficient. Our main result is that our conditions are indeed sufficient for large classes of examples, even when $M_\\Sigma$ and $\\beta M$ are not simply connected. We also investigate the space of such psc-metrics and show that it often splits into many cobordism classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-06T11:29:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "58J22",
      "53C27",
      "19L41",
      "55N22",
      "58J28"
    ],
    "keywords": [
      "positive scalar curvature",
      "spin pseudomanifolds",
      "secondary invariants",
      "fundamental group",
      "semisimple compact lie group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}