{
  "id": "2010.04320",
  "version": "v1",
  "published": "2020-10-09T01:31:07.000Z",
  "updated": "2020-10-09T01:31:07.000Z",
  "title": "The correspondence induced on the pillowcase by the earring tangle",
  "authors": [
    "Guillem Cazassus",
    "Christopher M. Herald",
    "Paul Kirk",
    "Artem Kotelskiy"
  ],
  "comment": "57 pages, 29 figures",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "The earring tangle consists of four strands 4pt x [0,1] inside S^2 x [0,1] and one meridian around one of the strands. Equipping this tangle with a nontrivial SO(3) bundle, we show that its traceless SU(2) flat moduli space is topologically a smooth genus three surface. We also show that the restriction map from this surface to the traceless flat moduli space of the boundary of the earring tangle is a particular Lagrangian immersion into the product of two pillowcases. The latter computation suggests that figure eight bubbling---a subtle degeneration phenomenon predicted by Bottman and Wehrheim---appears in the context of traceless character varieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-09T01:31:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K18",
      "57K31",
      "57R58",
      "81T13"
    ],
    "keywords": [
      "pillowcase",
      "bubbling-a subtle degeneration phenomenon",
      "correspondence",
      "traceless flat moduli space",
      "earring tangle consists"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}