{
  "id": "1210.2157",
  "version": "v3",
  "published": "2012-10-08T06:55:48.000Z",
  "updated": "2014-05-08T19:49:47.000Z",
  "title": "A coding-free simplicity criterion for the Lyapunov exponents of Teichmueller curves",
  "authors": [
    "Alex Eskin",
    "Carlos Matheus"
  ],
  "comment": "29 pages, 3 figures. Final version based on the referee's report. To appear in Geometriae Dedicata",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this note we show that the results of H. Furstenberg on the Poisson boundary of lattices of semisimple Lie groups allow to deduce simplicity properties of the Lyapunov spectrum of the Kontsevich-Zorich cocycle of Teichmueller curves in moduli spaces of Abelian differentials without the usage of codings of the Teichmueller flow. As an application, we show the simplicity of some Lyapunov exponents in the setting of (some) Prym Teichmueller curves of genus 4 where a coding-based approach seems hard to implement because of the poor knowledge of the Veech group of these Teichmueller curves. Finally, we extend the discussion in this note to show the simplicity of Lyapunov exponents coming from (high weight) variations of Hodge structures associated to mirror quintic Calabi-Yau threefolds.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-05-08T19:49:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lyapunov exponents",
      "coding-free simplicity criterion",
      "mirror quintic calabi-yau threefolds",
      "deduce simplicity properties",
      "prym teichmueller curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.2157E"
    }
  }
}