{
  "id": "1812.11867",
  "version": "v1",
  "published": "2018-12-31T16:06:22.000Z",
  "updated": "2018-12-31T16:06:22.000Z",
  "title": "$G_2$-instantons on noncompact $G_2$-manifolds: results and open problems",
  "authors": [
    "Jason Lotay",
    "Goncalo Oliveira"
  ],
  "comment": "To appear in a forthcoming volume of the Fields Institute Communications, entitled \"Lectures and Surveys on G2 manifolds and related topics\"",
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We survey the known existence and non-existence results for $G_2$-instantons on non-compact cohomogeneity-1 $G_2$-manifolds and their consequences, including an explicit example of a family of $G_2$-instantons where bubbling, removable singularities and conservation of energy phenomena occur. We also describe several open problems for future research.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-31T16:06:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C07",
      "53C25"
    ],
    "keywords": [
      "open problems",
      "instantons",
      "noncompact",
      "energy phenomena occur",
      "explicit example"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}