{
  "id": "2201.11434",
  "version": "v1",
  "published": "2022-01-27T10:43:55.000Z",
  "updated": "2022-01-27T10:43:55.000Z",
  "title": "Symmetric Cubic Laminations",
  "authors": [
    "Alexander Blokh",
    "Lex Oversteegen",
    "Nikita Selinger",
    "Vladlen Timorin",
    "Sandeep Chowdary Vejandla"
  ],
  "comment": "37 pages, 4 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "To investigate the degree $d$ connectedness locus, Thur\\-ston studied \\emph{$\\sigma_d$-invariant laminations}, where $\\sigma_d$ is the $d$-tupling map on the unit circle, and built a topological model for the space of quadratic polynomials $f(z) = z^2 +c$. In the spirit of Thurston's work, we consider the space of all \\emph{cubic symmetric polynomials} $f_\\lambda(z)=z^3+\\lambda^2 z$ in a series of three articles. In the present paper, the first in the series, we construct a lamination $C_sCL$ together with the induced factor space ${\\mathbb{S}}/C_sCL$ of the unit circle ${\\mathbb{S}}$. As will be verified in the third paper of the series, ${\\mathbb{S}}/C_sCL$ is a monotone model of the \\emph{cubic symmetric connected locus}, i.e. the space of all cubic symmetric polynomials with connected Julia sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-27T10:43:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F20",
      "37F10",
      "37F50"
    ],
    "keywords": [
      "symmetric cubic laminations",
      "unit circle",
      "cubic symmetric polynomials",
      "symmetric connected locus",
      "monotone model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}