On the growth of iterated monodromy groups
Abstract
Nekrashevych conjectured that the iterated monodromy groups of quadratic polynomials with preperiodic critical orbit have intermediate growth. We illustrate some of the difficulties that arise in attacking this conjecture and prove subexponential growth for the iterated monodromy group of z2+i. This is the first non-trivial example supporting the conjecture.
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