Iterated Monodromy Groups of Quadratic Polynomials, I

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'.

18 pages, 3 EPS figures

References in corpus (3)

• Amenability via random walks
• Thurston equivalence of topological polynomials
• Post-critically finite self-similar groups

Cited by in corpus (11)

• Classification of groups generated by 3-state automata over a 2-letter alphabet
• Profinite iterated monodromy groups arising from quadratic polynomials
• A nilpotent quotient algorithm for L-presented groups
• Finiteness and liftability of postcritically finite quadratic morphisms in arbitrary characteristic
• Boundary Values of the Thurston Pullback Map
• Finitely constrained groups of maximal Hausdorff dimension
• (Self-)similar groups and the Farrell-Jones conjectures
• Exponential growth of some iterated monodromy groups
• Orbit length generating functions of automorphisms of a rooted regular binary tree
• Mating, paper folding, and an endomorphism of PC^2
• Maximal subgroups of a family of iterated monodromy groups