JournalsggdVol. 2 , No. 3DOI 10.4171/ggd/42

Iterated monodromy groups of quadratic polynomials, I

  • Laurent Bartholdi

    Georg-August-Universität Göttingen, Germany
  • Volodymyr V. Nekrashevych

    Texas A&M University, College Station, United States
Iterated monodromy groups of quadratic polynomials, I cover

Abstract

We describe the iterated monodromy groups associated with post-critically finite quadratic polynomials, and make explicit their connection to the ‘kneading sequence’ of the polynomial.

We then give recursive presentations by generators and relations for these groups, and study some of their properties, like torsion and ‘branchness’.