Iterated Monodromy Groups of Quadratic Polynomials, I

preprint2008arXivOpen access

Abstract

We describe the iterated monodromy groups associated with post-critically finite quadratic polynomials, and 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'.

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