Kuang, Zheng (2018-08). Iterated Monodromy Groups of Rational Mappings. Master's Thesis. Thesis uri icon

abstract

  • We give the wreath recursion presentations of iterated monodromy groups of post-critically finite quadratic rational mappings fc whose ramification portrait are of the form 0 ? av2 ? ... ? avm ?1 ? ? ? 1 To find a pattern of these wreath recursions, we compute the wreath recursions of iterated monodromy groups of capture maps composed with the Basilica polynomial. This computation gives rise to the notion of addresses, which is used to represent wreath recursions. Then we conjecture that each capture map composed with the Basilica polynomial is topologically equivalent to a post-critically finite quadratic rational mapping, and thus we conclude that the iterated monodromy groups of fc can be represented by addresses.
  • We give the wreath recursion presentations of iterated monodromy groups of post-critically
    finite quadratic rational mappings fc whose ramification portrait are of the form
    0 ? av2 ? ... ? avm ?1 ? ? ? 1
    To find a pattern of these wreath recursions, we compute the wreath recursions of iterated monodromy
    groups of capture maps composed with the Basilica polynomial. This computation gives
    rise to the notion of addresses, which is used to represent wreath recursions. Then we conjecture
    that each capture map composed with the Basilica polynomial is topologically equivalent to a
    post-critically finite quadratic rational mapping, and thus we conclude that the iterated monodromy
    groups of fc can be represented by addresses.

publication date

  • August 2018
  • August 2018