{
  "id": "2103.15126",
  "version": "v1",
  "published": "2021-03-28T13:25:57.000Z",
  "updated": "2021-03-28T13:25:57.000Z",
  "title": "Oscillations and the Kontsevich-Zorich cocycle",
  "authors": [
    "Hamid Al-Saqban"
  ],
  "comment": "12 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We present a mechanism for producing oscillations along the lift of the Teichm\\\"uller geodesic flow to the (real) Hodge bundle, as the basepoint surface is deformed by a unipotent element of $\\text{SL}_2(\\mathbb{R})$. Invoking Chen-M\\\"oller, we apply our methods to all but finitely many strata in genus $4$, those exhibiting a varying Lyapunov-exponents phenomenon.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-28T13:25:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kontsevich-zorich cocycle",
      "geodesic flow",
      "hodge bundle",
      "basepoint surface",
      "unipotent element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}