{
  "id": "1409.5180",
  "version": "v1",
  "published": "2014-09-18T03:06:53.000Z",
  "updated": "2014-09-18T03:06:53.000Z",
  "title": "Affine Manifolds and Zero Lyapunov Exponents in Genus 3",
  "authors": [
    "David Aulicino"
  ],
  "comment": "34 pages",
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "In previous work, the author fully classified orbit closures in genus three with maximally many (four) zero Lyapunov exponents of the Kontsevich-Zorich cocycle. In this paper, we prove that there are no higher dimensional orbit closures in genus three with any zero Lyapunov exponents. Furthermore, if a Teichm\\\"uller curve in genus three has two zero Lyapunov exponents in the Kontsevich-Zorich cocycle, then it lies in the principal stratum and has at most quadratic trace field. Moreover, there can be at most finitely many such Teichm\\\"uller curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-18T03:06:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "zero lyapunov exponents",
      "affine manifolds",
      "higher dimensional orbit closures",
      "kontsevich-zorich cocycle",
      "author fully classified orbit closures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.5180A"
    }
  }
}