{
  "id": "1608.07789",
  "version": "v1",
  "published": "2016-08-28T09:13:02.000Z",
  "updated": "2016-08-28T09:13:02.000Z",
  "title": "$SU(2)^2$-invariant $G_2$-instantons",
  "authors": [
    "Jason D. Lotay",
    "Goncalo Oliveira"
  ],
  "comment": "57 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We initiate the systematic study of $G_2$-instantons with $SU(2)^2$-symmetry. As well as developing foundational theory, we give existence, non-existence and classification results for these instantons. We particularly focus on $\\mathbb{R}^4\\times S^3$ with its two known distinct holonomy $G_2$ metrics, which have different volume growths at infinity, exhibiting the different behaviour of instantons in these settings. We also give an explicit example of sequences of $G_2$-instantons where \"bubbling\" and \"removable singularity\" phenomena occur in the limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-28T09:13:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C07",
      "53C25"
    ],
    "keywords": [
      "instantons",
      "systematic study",
      "developing foundational theory",
      "classification results",
      "distinct holonomy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}