{
  "id": "1209.2854",
  "version": "v2",
  "published": "2012-09-13T11:23:16.000Z",
  "updated": "2014-12-04T04:59:52.000Z",
  "title": "Symplectic and Isometric SL(2,R) invariant subbundles of the Hodge bundle",
  "authors": [
    "Artur Avila",
    "Alex Eskin",
    "Martin Moeller"
  ],
  "comment": "23 pages. To appear in Crelle's journal",
  "categories": [
    "math.DS",
    "math.AG",
    "math.GT"
  ],
  "abstract": "Suppose N is an affine SL(2,R)-invariant submanfold of the moduli space of pairs (M,w) where M is a curve, and w is a holomorphic 1-form on M. We show that the Forni bundle of N (i.e. the maximal SL(2,R)-invariant isometric subbundle of the Hodge bundle of N) is always flat and is always orthogonal to the tangent space of N. As a corollary, it follows that the Hodge bundle of N is semisimple.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-13T11:23:16.000Z",
      "comment": "16 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-04T04:59:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hodge bundle",
      "isometric sl",
      "invariant subbundles",
      "symplectic",
      "affine sl"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.2854A"
    }
  }
}