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’.
Cite this article
Laurent Bartholdi, Volodymyr V. Nekrashevych, Iterated monodromy groups of quadratic polynomials, I. Groups Geom. Dyn. 2 (2008), no. 3, pp. 309–336DOI 10.4171/GGD/42