Groups, Geometry, and Dynamics


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Volume 2, Issue 3, 2008, pp. 309–336
DOI: 10.4171/GGD/42

Iterated monodromy groups of quadratic polynomials, I

Laurent Bartholdi[1] and Volodymyr V. Nekrashevych[2]

(1) Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstraße 3–5, 37073, GÖTTINGEN, GERMANY
(2) Department of Mathematics, Texas A&M University, TX 77843-3368, COLLEGE STATION, UNITED STATES

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’.

Keywords: Iterated monodromy groups, quadratic polynomials, automata groups, kneading sequences, recursive presentations

Bartholdi Laurent, Nekrashevych Volodymyr: Iterated monodromy groups of quadratic polynomials, I. Groups Geom. Dyn. 2 (2008), 309-336. doi: 10.4171/GGD/42